In recent years, warm dark matter models have been studied as a viable alternative to the cold dark matter models. The warm dark matter particle properties are expected to imprint distinct signatures on the structure formation at both large and small scales and there have been many attempts to study these properties with numerical simulations. In this paper, we review and update on warm dark matter simulation studies from the past two decades and their most significant results: structure formation mechanisms, halos evolution, sizes and distribution, and internal structure properties. We discuss the theoretical assumptions and the limitations of the methods employed. In this context, several controversial claims are scrutinized in the attempt to clarify these confusing and sometimes even contradictory conclusions in the numerical simulation literature. We address the circumstances in which a promising keV dark matter candidate should be properly treated in the simulations.