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I would appreciate if someone could recommend me good review literature on the density matrix renormalization group (DMRG) method, especially for magnetic systems.

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There is also this website which attempts (seemingly very successfully!) to track every DMRG, MPS, TPS, MERA, and/or general Tensor Network paper ever.

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    $\begingroup$ I vote for 2004: Reviews of Modern Physics by Ulrich Schollwoeck, which is long but comprehensive. $\endgroup$ – Yingzhou Li May 6 at 20:51
  • $\begingroup$ Schollwöck is actually 2005, journals.aps.org/rmp/abstract/10.1103/RevModPhys.77.259 $\endgroup$ – Susi Lehtola Jun 30 at 9:19
  • $\begingroup$ on arXiv it says "accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the January 2005 issue". Perhaps I can change my answer so that it says 2005, but one should know that this review covers only material up to 2004. $\endgroup$ – Nike Dattani Jun 30 at 16:37
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There's two later review articles by Schollwöck that weren't in Nike's excellent list:

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