See the Motives volumes, especially the first 4 articles in volume 2.
Oberwolfach reports 1 (2004) no 4, on Polylogarithms
Lewin: Structural properties of polylogaritms (book). Also other book by same author??
See Goncharov in K-theory handbook.
http://www.math.uiuc.edu/K-theory/0261: Classical motivic polylogarithm according to Beilinson and Deligne.
Hanamura and MacPherson: Geometric construction of polylogarithms, I and II (1993 and 1996)
Abstracts from a workshop are here
Don Zagier, Polylogarithms, Dedekind zeta functions and the algebraic -theory of fields
Here is a sample article. Another one, and something by Goncharov
MR1290822 (95i:81224) Kirillov, A. N.(4-CAMB-NI) Dilogarithm identities, partitions, and spectra in conformal field theory. (English summary) Algebra i Analiz 6 (1994), no. 2, 152–175; translation in St. Petersburg Math. J. 6 (1995), no. 2, 327–348
MR1312980 (96b:19007) Goncharov, A. B.(1-MIT) Chow polylogarithms and regulators. Math. Res. Lett. 2 (1995), no. 1, 95–112.
MR1348706 (96g:19005) Goncharov, A. B.(1-MIT) Geometry of configurations, polylogarithms, and motivic cohomology. Adv. Math. 114 (1995), no. 2, 197–318.
Nice survey: MR1354171 (97a:19005) Borel, Armand(1-IASP) Values of zeta-functions at integers, cohomology and polylogarithms. Current trends in mathematics and physics, 1–44, Narosa, New Delhi, 1995.
MR1385924 (97h:19009) Gangl, Herbert(D-BONN-MN) Funktionalgleichungen von Polylogarithmen. (German) [Functional equations of polylogarithms]
MR1443532 (98d:11073) Wildeshaus, Jörg(D-MUNS) On an elliptic analogue of Zagier’s conjecture. Duke Math. J. 87 (1997), no. 2, 355–407.
MR1653320 (2000c:11108) Goncharov, A. B.(1-BRN) Multiple polylogarithms, cyclotomy and modular complexes. Math. Res. Lett. 5 (1998), no. 4, 497–516.
A. B. Goncharov, Geometry of the trilogarithm and the motivic Lie algebra of a field
A good path to an overview of polylogs could be checking everything by Goncharov, and all references in reviews of Goncharov.
arXiv:1210.2358 Classical Polylogarithm – Abstract of a series of lectures given at the workshop on polylogs in Essen, May 1 – 4, 1997 fra arXiv Front: math.AG av Annette Huber, Jörg Wildeshaus These are extended abstracts from an series of lectures in 1997. The text has not been updated since then
We explain the construction of the motivic polylog as published in Annette Huber, Jörg Wildeshaus, Classical Motivic Polylogarithm According to Beilinson and Deligne, Doc.Math.J.DMV 3 (1998) 27-133. The main application is a comparison result for cyclotomic elements needed in the proof of the Tamagawa number conjecture of Bloch and Kato for Dirichlet characters. The exposition concentrates on the Hodge theoretic part of the story.
arXiv:0908.2238 A simple construction of Grassmannian polylogarithms from arXiv Front: math.AG by A. B. Goncharov We give a simple explicit construction of the Grassmannian n-logarithm, which is a multivalued analytic function on the quotient of the Grassmannian of generic n-dimensional subspaces in 2n-dimensional coordinate complex vector space by the action of the 2n-dimensional coordinate torus
We study Tate iterated integrals, which are homotopy invariant integrals of 1-forms dlog(rational functions). We introduce the Hopf algebra of integrable symbols related to an algebraic variety, which controls the Tate iterated integrals We give a simple explicit formula for the Tate iterated integrals related to the Grassmannian polylogarithms.
nLab page on Polylogarithm