In The Unicode Standard, Punctuation marks are discussed in  Chapter 6 Writing Systems and Punctuation. Punctuation marks can generally be used across scripts. They tend to be scattered across various blocks in Unicode. Some scripts have punctuation marks which are specific to that script and those are generally encoded with the script block(s).

Punctuation (not script specific) is now encoded in the following blocks:

BlocksCharacter RangeAdded in Unicode VersionDocumentation
Basic Latin 0000..007F 1.0  U0000.pdf
Latin-1 Supplement 0080..00FF 1.0  U0080.pdf
General Punctuation 2000..206F 1.0  U2000.pdf
Supplemental Punctuation 2E00..2E7F 4.1  U2E00.pdf
CJK Symbols and Punctuation block 3000..303F 1.1  U3000.pdf
Vertical Forms FE10..FE1F 4.1  UFE10.pdf
CJK Compatibility Forms FE30..FE4F 1.1  UFE30.pdf
Small Form Variants FE50..FE6F 1.1  UFE50.pdf
Halfwidth and Fullwidth Forms FF00..FFEF 1.1  UFF00.pdf

Subsequent to version 1.1, the following characters have been added to common punctuation:

CharactersUnicode VersionDocumentation
202F 3.0
2047 3.2  n2092.pdf
2048..204D 3.0
204E..2050 3.2
2051 3.2  n2092.pdf
2052 3.2
2053..2054 4.0
2055 4.1
2056 4.1  n2610r.pdf L2/03-282
2057 3.2
2058..2059 4.1  n2610r.pdf L2/03-282,  n2642.pdf L2/03-324
205A..205C 4.1  
205D 4.1  n2642.pdf L2/03-324
205E 4.1
205F 3.2
2060..2063 3.2
2064 5.1  n3198.pdf L2/07-011R2
2E00..2E0C 4.1  n2612-1.pdf L2/03-074 R2
2E0D 4.1  n2675.pdf
2E0E..2E16 4.1  n2642.pdf L2/03-324
2E17 4.1  n2647.pdf L2/03-338
2E18 5.1  n2935.pdf L2/05-086
2E19 5.1  n3218.pdf L2/06-269
2E1A..2E1B 5.1  n3193.pdf L2/07-004
2E1C..2E1D 4.1  n2765.pdf L2/04-172
2E1E..2E2E 5.1  n3193.pdf L2/07-004
2E2F 5.1
2E30 5.1  n3193.pdf L2/07-004
2E31 5.2
2E45..2E49 10.0  
2E4C pending  L2/16-220
2E4D..2E4E pending  L2/16-219

Documentation refers to  ISO Working Group and Unicode proposals

A number of proposals for its inclusion have been submitted to the Unicode Technical Committee and WG2:

1999-07-24 On the apostrophe and quotation mark, with a note on Egyptian transliteration characters — Michael Everson ( WG2 N2043,  L2/99-246)
1999-12-01 On the need for a ZERO-WIDTH LIGATOR — Michael Everson ( WG2 N2141,  L2/99-379)
2000-01-04 U-301C WAVE DASH — Japan NB ( WG2 N2166.doc,  L2/00-065)
2000-01-06 Further discussion of the ZERO-WIDTH LIGATOR — Michael Everson ( WG2 N2147,  L2/00-012)

2000-01-24 ZWJ contradictions, ZWL — Ken Whistler, Lloyd Anderson ( L2/00-023)

2000-01-25 Extending ZWJ and ZWNJ for Ligation — Mark Davis ( L2/00-025)

2000-01-25 Five comments on ZWL and ZWJ — Lloyd Anderson ( L2/00-026)

2000-01-31 Comments on Ligature Control — John Jenkins ( L2/00-031)

2000-03-31 Supplemental terminal graphics for Unicode — Frank da Cruz ( L2/00-159)

2000-04-30 Zero width grapheme joiner — Mark Davis ( L2/00-156)

2000-08-09 Proposal for addition of ZERO WIDTH WORD JOINER (WG2 N2335) — Mark Davis ( WG2 N2235.htm,  L2/00-258)

2000-09-15 SOFT HYPHEN and some other characters — Kent Karlsson (WG2 N2268,  L2/00-332)

2001-04-10 Bracket Disunification & Normalization Hell — Ken Whistler ( L2/01-168)

2002-01-21 TLG: Miscellanea Proposal — TLG (D. Anderson) ( L2/02-031)

2002-01-21 TLG: Background & detail information (208k, 26pp) — TLG (D. Anderson) ( L2/02-033)

2002-07-30 Proposal to add a few dashes — Eric Muller ( L2/02-277)

2002-08-14 Yes, SOFT HYPHEN is a hard problem — Eric Muller ( L2/02-279)

2002-10-22 Em-dash comments (from web reporting form) — Donald Figge ( L2/02-349)

2002-10-23 Dashes — Mark Davis ( L2/02-350)

2002-10-23 Dashes — Patrick Andries ( L2/02-352)

2002-10-24 Dashes — Ken Whistler ( L2/02-353)

2002-10-25 Dashes — Eric Muller ( L2/02-357)

2002-10-28 Response to using ZWJ and ZWNJ to control ligatures — Ayman Aldahleh, Paul Nelson ( L2/02-363)

2002-11-27 Note on soft hyphens in 10646/Unicode — Kent Karlsson ( WG2 N2531,  L2/02-426)

2002-12-02 Answer to L2/02-426, SC2/WG2 N2531 — Eric Muller ( L2/02-444)

2003-01-30 Response to "UTC Agenda Item: Scope of Enclosing Marks" — Asmus Freytag ( L2/03-028)

2003-06-11 Proposal to encode additional Punctuation Characters in the UCS — Maria Pantelia / TLG ( WG2 N2612-7,  L2/03-193)

2003-08-21 ZWJ/ZWNJ proposed general category change — Kent Karlsson ( L2/03-276)

2003-10-06 Proposal to encode additional Greek editorial and punctuation characters in the UCS — Maria Pantelia / TLG ( WG2 N2642,  L2/03-324)

2003-10-10 Proposal — Symbols used in dictionaries — Asmus Freytag ( WG2 N2655)

2003-10-13 Further discussion of the Double Oblique Hyphen — MIchael Everson ( WG2 N2647,  L2/03-338)

2003-10-19 Background on DOUBLE OBLIQUE HYPHEN — Deborah Anderson ( L2/03-347)

2003-10-22 Proposal to add one punctuation character to the UCS — Michael Everson ( WG2 N2675, L2/03-379)

2004-03-04 Proposal to add two Masoretic punctuation marks to the BMP of the UCS — Mark Shoulson, Peter Kirk, John Hudson, Michael Everson, Peter Constable ( WG2 N2714,  L2/04-089)

2004-06-02 Romanian Proposal for ISO/IEC 6937 Amendment — Romanian N B ( WG2 N2783,  L2/04-205)

2006-08-01 Proposal to Add Additional Ancient Roman Characters to UCS — David Perry ( WG2 N3218,  L2/06-269)

2007-01-09 Proposal to add Medievalist and Iranianist punctuation characters to the UCS — Michael Everson, Peter Baker, Marcus Dohnicht, António Emiliano, Odd Einar Haugen, Susana Pedro, David J. Perry, Roozbeh Pournader ( WG2 N3193,  L2/07-004)

2007-08-02 Middle Dots and Don'ts — Ken Whistler ( L2/07-258)

2007-09-18 Proposal to Encode WORD SEPARATOR MIDDLE DOT — US N.B. ( WG2 N3347,  L2/07-320)

2008-09-06 Proposal to Revert to the Original Properties of the Zero Width Space — Javier Solá ( L2/08-344)

2009-12-05 Proposal to encode six punctuation characters in the UCS — Michael Everson ( WG2 N3740,  L2/09-425)

2010-02-10 Proposal to encode two dashes required by the Chicago Manual of Style in the UCS — Karl Pentzlin ( WG2 N3770,  L2/10-037)

2010-05-04 Proposal to encode a punctuation mark "Double Hyphen" — Karl Pentzlin ( L2/10-162)

2010-06-17 Oblique hyphen vs. Double Hyphen — Asmus Freytag ( L2/10-214)

2010-07-29 Comments on the Public Review Issue #169 "Glyph Variation of Double Oblique Hyphen" — Karl Pentzlin ( L2/10-269)

2010-09-28 Revised Proposal to encode a punctuation mark "Double Hyphen" — Karl Pentzlin ( WG2 N3917,  L2/10-361)

2011-01-17 Revised Proposal to encode a punctuation mark "Double Hyphen" — German N.B. ( WG2 N3983,  L2/11-038)

2011-02-02 Notes on the naming of some characters proposed in the FCD of ISO/IEC 10646:2012 — Karl Pentzlin ( WG2 N3984,  L2/11-057)

2011-10-17 Proposal to encode a Low One Dot Leader in the UCS — Martin Schrage, Karl Pentzlin ( WG2 N4209,  L2/11-364)

2012-04-27 Punctuation symbols — Mark Davis ( L2/12-146)

2012-05-03 Request to correct the LineBreak.txt entry for U+2E3A TWO-EM DASH — Karl Pentzlin ( L2/12-170)

2012-05-09 Proposal to encode SENTENCE SEPARATOR (NON-JOINER) and SENTENCE JOINER — Arle Lommel ( L2/12-119)

2012-10-01 Revised Proposal to encode six punctuation characters introduced by Hervé Bazin in the UCS — Mykyta Yevstifeyev, Karl Pentzlin ( WG2 N4256,  L2/11-232)

2013-09-23 Proposal to Encode a Slavonic Punctuation Mark in Unicode — Aleksandr Andreev, Yuri Shardt, Nikita Simmons ( L2/13-140)

2013-10-06 LB Fix LB status for Floor/Ceiling characters — Mark Davis ( L2/13-184)

2013-11-01 Expert Feedback on L2/13-140 SLAVONIC PARAGRAPHOS — Stephen Emmel, Jost Gippert ( L2/13-212)

2013-11-21 Catalan MIDDLEDOT and UAX #31 — Joan Montané ( L2/13-239)

2013-12-16 Precomposed punctuation proposal — Kirill Larionov ( L2/13-237)

2013-12-16 Proposal to Encode a Slavonic Punctuation Mark in Unicode — Aleksandr Andreev, Yuri Shardt, Nikita Simmons ( L2/13-238)

2014-02-04 Proposal to Encode a Slavonic Punctuation Mark in Unicode — Aleksandr Andreev, Yuri Shardt, Nikita Simmons ( WG2 N4534)

2014-07-18 Proposal to encode GREEK BYZANTINE DOUBLE SUSPENSION MARK — Dumbarton Oaks (Joel Kalvesmaki) ( WG2 N4595.doc,  L2/14-157)

2014-08-06 Proposal for the modification of the sample character layout of WAVE_DASH (U+301C) — Hiroyuki Komatsu ( WG2 N4606,  L2/14-198)

2014-12-12 Short hyphen proposal — William G. Moore ( L2/14-302)

2015-02-04 Line break property value of U+22EF MIDLINE HORIZONTAL ELLIPSIS — Peter Edberg ( L2/15-077)

2015-07-29 Proposal to Encode some Additional Symbols used in Church Slavonic Text — Aleksandr Andreev, Yuri Shardt, Nikita Simmons ( L2/15-173)

2015-10-31 Property Change for U+202F NARROW NO-BREAK SPACE (PRI #308 background) — UTC / Peter Edberg ( L2/15-295)

UTC #146 Minutes ( L2/16-004) (See B.11.6.2 for decision and action items)

2015-12-19 Proposal to add Medievalist punctuation characters — Michael Everson (editor), Peter Baker, Florian Grammel, Odd Einar Haugen (WG2 N4704,  L2/15-327)

UTC #146 Minutes ( L2/16-004) (See C.5 for decision and action items)

2016-07-30 Feedback and Evidence on Medievalist punctuation characters (L2/16‐125) — Deborah Anderson ( L2/16-219)

UTC #148 Minutes ( L2/16-203) (See C.14.2 for decision and action items)

2016-08-01 Proposal to encode MEDIEVAL COMMA — Michael Everson, Deborah Anderson, et al ( L2/16-220)

UTC #148 Minutes ( L2/16-203) (See C.14.3 for decision and action items)

2016-08-04 Proposal to encode PARAGRAPHUS and PUNCTUS ELEVATUS — Michael Everson, Deborah Anderson, et al ( L2/16-235)

UTC #148 Minutes ( L2/16-203) (See C.14.4 for decision and action items)