The present master thesis is concerned with the multidimensional multiple-choice knapsack problem (MMKP). The objective of this literature review is to give an overview of existing methods of solution methods. The Knapsack problem is NP-hard. Therefore it's not to be expected, that there is an algorithm that solves the knapsack problem optimally in polynomial time. Unlike other knapsack problems for the multidimensional multiple-choice knapsack problem (MMKP) finding a feasible solution is not trivial. In the worst case, all possible combinations have to be checked. Since solving these problems generally needs a lot of effort, many of the existing algorithms are relatively new. Chapter two gives an introduction to the knapsack problem as such. In addition, different types of knapsack problems are presented which have relevance in solution methods for the MMKP: the 0-1 knapsack problem (KP), the multidimensional knapsack problem (MDKP) and the multiple-choice knapsack problem (MCKP). Chapter three presents the multidimensional multiple-choice knapsack problem (MMKP). In chapters two and three, the notation as used in the description the various methods, is introduced. Chapter four examines algorithms to obtain exact solutions for the multidimensional multiple-choice knapsack problem. The three known in the literature are thoroughly investigated: the "BBLP" algorithm, the "EMKP" algorithm and a core concept. All these approaches are based on a branch and bound method. The typical search tree is built, however, in different ways.Chapter five treats heuristics. Some of the algorithms are described in detail. Thus, a well-known approach based on Lagrange multipliers by Moser et al., an ant colony optimization (ACO)-based algorithm and the "HMMKP" algorithm are presented in detail. Some other algorithms are only briefly outlined.