If I'm not mistaken, the claim of the Catholic Church is that Papal Succession is unbroken all the way back to Peter.
Is there a list of popes and the history from Peter to the present day? If so, where can I find it?
And just so that your answer isn't a link-only answer, frowned upon on SE sites, maybe include the list if you can copy/paste it as well as citing the source
Here's the List of Popes from newadvent.org, which I assume is the same list found in many US Catholic-approved Bibles, with the exception of the Papal "oppositions" listed here:
1. St. Peter (32-67)
2. St. Linus (67-76)
3. St. Anacletus (Cletus) (76-88)
4. St. Clement I (88-97)
5. St. Evaristus (97-105)
6. St. Alexander I (105-115)
7. St. Sixtus I (115-125) Also called Xystus I
8. St. Telesphorus (125-136)
9. St. Hyginus (136-140)
10. St. Pius I (140-155)
11. St. Anicetus (155-166)
12. St. Soter (166-175)
13. St. Eleutherius (175-189)
14. St. Victor I (189-199)
15. St. Zephyrinus (199-217)
16. St. Callistus I (217-22) Callistus and the following three popes were opposed by St. Hippolytus, antipope (217-236)
17. St. Urban I (222-30)
18. St. Pontain (230-35)
19. St. Anterus (235-36)
20. St. Fabian (236-50)
21. St. Cornelius (251-53) Opposed by Novatian, antipope (251)
22. St. Lucius I (253-54)
23. St. Stephen I (254-257)
24. St. Sixtus II (257-258)
25. St. Dionysius (260-268)
26. St. Felix I (269-274)
27. St. Eutychian (275-283)
28. St. Caius (283-296) Also called Gaius
29. St. Marcellinus (296-304)
30. St. Marcellus I (308-309)
31. St. Eusebius (309 or 310)
32. St. Miltiades (311-14)
33. St. Sylvester I (314-35)
34. St. Marcus (336)
35. St. Julius I (337-52)
36. Liberius (352-66) Opposed by Felix II, antipope (355-365)
37. St. Damasus I (366-83) Opposed by Ursicinus, antipope (366-367)
38. St. Siricius (384-99)
39. St. Anastasius I (399-401)
40. St. Innocent I (401-17)
41. St. Zosimus (417-18)
42. St. Boniface I (418-22) Opposed by Eulalius, antipope (418-419)
43. St. Celestine I (422-32)
44. St. Sixtus III (432-40)
45. St. Leo I (the Great) (440-61)
46. St. Hilarius (461-68)
47. St. Simplicius (468-83)
48. St. Felix III (II) (483-92)
49. St. Gelasius I (492-96)
50. Anastasius II (496-98)
51. St. Symmachus (498-514) Opposed by Laurentius, antipope (498-501)
52. St. Hormisdas (514-23)
53. St. John I (523-26)
54. St. Felix IV (III) (526-30)
55. Boniface II (530-32) Opposed by Dioscorus, antipope (530)
56. John II (533-35)
57. St. Agapetus I (535-36) Also called Agapitus I
58. St. Silverius (536-37)
59. Vigilius (537-55)
60. Pelagius I (556-61)
61. John III (561-74)
62. Benedict I (575-79)
63. Pelagius II (579-90)
64. St. Gregory I (the Great) (590-604)
65. Sabinian (604-606)
66. Boniface III (607)
67. St. Boniface IV (608-15)
68. St. Deusdedit (Adeodatus I) (615-18)
69. Boniface V (619-25)
70. Honorius I (625-38)
71. Severinus (640)
72. John IV (640-42)
73. Theodore I (642-49)
74. St. Martin I (649-55)
75. St. Eugene I (655-57)
76. St. Vitalian (657-72)
77. Adeodatus (II) (672-76)
78. Donus (676-78)
79. St. Agatho (678-81)
80. St. Leo II (682-83)
81. St. Benedict II (684-85)
82. John V (685-86)
83. Conon (686-87)
84. St. Sergius I (687-701) Opposed by Theodore and Paschal, antipopes (687)
85. John VI (701-05)
86. John VII (705-07)
87. Sisinnius (708)
88. Constantine (708-15)
89. St. Gregory II (715-31)
90. St. Gregory III (731-41)
91. St. Zachary (741-52)
92. Stephen II (752) Because he died before being consecrated, many authoritative lists omit him
93. Stephen III (752-57)
94. St. Paul I (757-67)
95. Stephen IV (767-72) Opposed by Constantine II (767) and Philip (768), antipopes (767)
96. Adrian I (772-95)
97. St. Leo III (795-816)
98. Stephen V (816-17)
99. St. Paschal I (817-24)
100. Eugene II (824-27)
101. Valentine (827)
102. Gregory IV (827-44)
103. Sergius II (844-47) Opposed by John, antipope (855)
104. St. Leo IV (847-55)
105. Benedict III (855-58) Opposed by Anastasius, antipope (855)
106. St. Nicholas I (the Great) (858-67)
107. Adrian II (867-72)
108. John VIII (872-82)
109. Marinus I (882-84)
110. St. Adrian III (884-85)
111. Stephen VI (885-91)
112. Formosus (891-96)
113. Boniface VI (896)
114. Stephen VII (896-97)
115. Romanus (897)
116. Theodore II (897)
117. John IX (898-900)
118. Benedict IV (900-03)
119. Leo V (903) Opposed by Christopher, antipope (903-904)
120. Sergius III (904-11)
121. Anastasius III (911-13)
122. Lando (913-14)
123. John X (914-28)
124. Leo VI (928)
125. Stephen VIII (929-31)
126. John XI (931-35)
127. Leo VII (936-39)
128. Stephen IX (939-42)
129. Marinus II (942-46)
130. Agapetus II (946-55)
131. John XII (955-63)
132. Leo VIII (963-64)
133. Benedict V (964)
134. John XIII (965-72)
135. Benedict VI (973-74)
136. Benedict VII (974-83) Benedict and John XIV were opposed by Boniface VII, antipope (974; 984-985)
137. John XIV (983-84)
138. John XV (985-96)
139. Gregory V (996-99) Opposed by John XVI, antipope (997-998)
140. Sylvester II (999-1003)
141. John XVII (1003)
142. John XVIII (1003-09)
143. Sergius IV (1009-12)
144. Benedict VIII (1012-24) Opposed by Gregory, antipope (1012)
145. John XIX (1024-32)
146. Benedict IX (1032-45) He appears on this list three separate times, because he was twice deposed and restored
147. Sylvester III (1045) Considered by some to be an antipope
148. Benedict IX (1045)
149. Gregory VI (1045-46)
150. Clement II (1046-47)
151. Benedict IX (1047-48)
152. Damasus II (1048)
153. St. Leo IX (1049-54)
154. Victor II (1055-57)
155. Stephen X (1057-58)
156. Nicholas II (1058-61) Opposed by Benedict X, antipope (1058)
157. Alexander II (1061-73) Opposed by Honorius II, antipope (1061-1072)
158. St. Gregory VII (1073-85) Gregory and the following three popes were opposed by Guibert ("Clement III"), antipope (1080-1100)
159. Blessed Victor III (1086-87)
160. Blessed Urban II (1088-99)
161. Paschal II (1099-1118) Opposed by Theodoric (1100), Aleric (1102) and Maginulf ("Sylvester IV", 1105-1111), antipopes (1100)
162. Gelasius II (1118-19) Opposed by Burdin ("Gregory VIII"), antipope (1118)
163. Callistus II (1119-24)
164. Honorius II (1124-30) Opposed by Celestine II, antipope (1124)
165. Innocent II (1130-43) Opposed by Anacletus II (1130-1138) and Gregory Conti ("Victor IV") (1138), antipopes (1138)
166. Celestine II (1143-44)
167. Lucius II (1144-45)
168. Blessed Eugene III (1145-53)
169. Anastasius IV (1153-54)
170. Adrian IV (1154-59)
171. Alexander III (1159-81) Opposed by Octavius ("Victor IV") (1159-1164), Pascal III (1165-1168), Callistus III (1168-1177) and Innocent III (1178-1180), antipopes
172. Lucius III (1181-85)
173. Urban III (1185-87)
174. Gregory VIII (1187)
175. Clement III (1187-91)
176. Celestine III (1191-98)
177. Innocent III (1198-1216)
178. Honorius III (1216-27)
179. Gregory IX (1227-41)
180. Celestine IV (1241)
181. Innocent IV (1243-54)
182. Alexander IV (1254-61)
183. Urban IV (1261-64)
184. Clement IV (1265-68)
185. Blessed Gregory X (1271-76)
186. Blessed Innocent V (1276)
187. Adrian V (1276)
188. John XXI (1276-77)
189. Nicholas III (1277-80)
190. Martin IV (1281-85)
191. Honorius IV (1285-87)
192. Nicholas IV (1288-92)
193. St. Celestine V (1294)
194. Boniface VIII (1294-1303)
195. Blessed Benedict XI (1303-04)
196. Clement V (1305-14)
197. John XXII (1316-34) Opposed by Nicholas V, antipope (1328-1330)
198. Benedict XII (1334-42)
199. Clement VI (1342-52)
200. Innocent VI (1352-62)
201. Blessed Urban V (1362-70)
202. Gregory XI (1370-78)
203. Urban VI (1378-89) Opposed by Robert of Geneva ("Clement VII"), antipope (1378-1394)
204. Boniface IX (1389-1404) Opposed by Robert of Geneva ("Clement VII") (1378-1394), Pedro de Luna ("Benedict XIII") (1394-1417) and Baldassare Cossa ("John XXIII") (1400-1415), antipopes
205. Innocent VII (1404-06) Opposed by Pedro de Luna ("Benedict XIII") (1394-1417) and Baldassare Cossa ("John XXIII") (1400-1415), antipopes
206. Gregory XII (1406-15) Opposed by Pedro de Luna ("Benedict XIII") (1394-1417), Baldassare Cossa ("John XXIII") (1400-1415), and Pietro Philarghi ("Alexander V") (1409-1410), antipopes
207. Martin V (1417-31)
208. Eugene IV (1431-47) Opposed by Amadeus of Savoy ("Felix V"), antipope (1439-1449)
209. Nicholas V (1447-55)
210. Callistus III (1455-58)
211. Pius II (1458-64)
212. Paul II (1464-71)
213. Sixtus IV (1471-84)
214. Innocent VIII (1484-92)
215. Alexander VI (1492-1503)
216. Pius III (1503)
217. Julius II (1503-13)
218. Leo X (1513-21)
219. Adrian VI (1522-23)
220. Clement VII (1523-34)
221. Paul III (1534-49)
222. Julius III (1550-55)
223. Marcellus II (1555)
224. Paul IV (1555-59)
225. Pius IV (1559-65)
226. St. Pius V (1566-72)
227. Gregory XIII (1572-85)
228. Sixtus V (1585-90)
229. Urban VII (1590)
230. Gregory XIV (1590-91)
231. Innocent IX (1591)
232. Clement VIII (1592-1605)
233. Leo XI (1605)
234. Paul V (1605-21)
235. Gregory XV (1621-23)
236. Urban VIII (1623-44)
237. Innocent X (1644-55)
238. Alexander VII (1655-67)
239. Clement IX (1667-69)
240. Clement X (1670-76)
241. Blessed Innocent XI (1676-89)
242. Alexander VIII (1689-91)
243. Innocent XII (1691-1700)
244. Clement XI (1700-21)
245. Innocent XIII (1721-24)
246. Benedict XIII (1724-30)
247. Clement XII (1730-40)
248. Benedict XIV (1740-58)
249. Clement XIII (1758-69)
250. Clement XIV (1769-74)
251. Pius VI (1775-99)
252. Pius VII (1800-23)
253. Leo XII (1823-29)
254. Pius VIII (1829-30)
255. Gregory XVI (1831-46)
256. Blessed Pius IX (1846-78)
257. Leo XIII (1878-1903)
258. St. Pius X (1903-14)
259. Benedict XV (1914-22) Biographies of Benedict XV and his successors will be added at a later date
260. Pius XI (1922-39)
261. Pius XII (1939-58)
262. Blessed John XXIII (1958-63)
263. Paul VI (1963-78)
264. John Paul I (1978)
265. John Paul II (1978-2005)
266. Benedict XVI (2005—)
The current, official Vatican list of popes from Peter to the present follows at the end of this answer. However it is not as simple as that, because to some extent it really only represents the Vatican politics of the present time.
Christopher was listed as a legitimate pope (October 903 to January 904) in most modern lists of Popes until the first half of the 20th century, when he was relegated to the status of antipope.
Some consider Sylvester III to have been an antipope, although he continues to be listed as an official Pope (1045) in Vatican lists.
Benedict X (1058-1059) was still regarded as a legitimate pope three hundred years later when Nicola Boccasini took the name Benedict XI (1303-1304). Benedict X is now regarded as an antipope, meaning that there is no Pope Benedict X in the present list.
John W. O’Malley, S.J. says, in A History of the Popes, page 147, there is a portfolio called the Libri de Schismate (Documents on the Schism), a collection of testimonies and arguments from contemporaries, in the Vatican Archives. Examination of this has consistently proved inconclusive for deciding who was the rightful pope at the time of the Western Schism in 1379. The Catholic church has never made a formal pronouncement on the claimants, but especially in the past hundred years the Holy See has in the lists of popes it regularly publishes always sided with the Roman claimant, Urban VI, over the Avignonese claimant, Clement.
Finally, there is some doubt about the historicity of popes prior to the middle of the second century, with Anicetus (155-166) the earliest person certain to have been elected bishop of Rome with monarchical authority, although Pius I (140-155) might also have held the office before him. Francis A. Sullivan S.J. says in From Apostles to Bishops, page 15, there exists a broad consensus among scholars, including most Catholic ones, that such churches as at Rome most probably continued to be led for some time by a college of presbyters, and that only during the course of the second century did the threefold structure become generally the rule, with a bishop, assisted by presbyters, presiding over each local church. There is no certain evidence that Peter ever went to Rome, although Sullivan believes he probably did.
(from the Catholic Encyclopedia)
