Voting is one of the several methods for making group decisions. A large number of voting systems have been developed for a seemingly same purpose, i.e., to find out the collective will. The basic motivation for the study of voting systems is the fact that different systems often produce different outcomes when applied to a given set of voter opinions. In some contexts we are able to single out plausible outcomes, e.g., candidates who – given a distribution of opinions in the electorate – ought to be elected for the system to be called reasonable or democratic in some specific sense. Social choice theorists have developed various plausibility criteria for the evaluation of voting systems. After discussing the classic paradoxes of social choice, we review the main criteria as well as the most important results in social choice theory. We also present some techniques for the analysis of opinion distributions. Finally, we discuss some profile restrictions and their relevance for the voting system choice.