After the seminal books by Martello and Toth (1990) and Kellerer, Pferschy, and Pisinger (2004), knapsack problems became a classical and rich research area in combinatorial optimization . The purpose of this survey, structured in two parts, is to cover the developments appeared in this field after the publication of the latter volume. Part I treats the classical single knapsack problems and their variants. The present Part II covers multiple, multidimensional, and quadratic knapsack problems, as well as other relevant variants, such as, e.g., multiobjective and online versions.