The nature of dark matter constitutes one of the biggest questions in physics, cosmology and astronomy. This thesis explores dark matter hypothesized models, with a focus on warm dark matter models, from both theoretical and numerical simulations perspectives, with the purpose of constraining the dark matter particle candidates. Using high-resolution simulations I have studied the effect of warm dark matter properties on large-scale structure - structure formation and evolution and small-scale structure – internal properties of dark matter halos. The results show that structure formation is qualitatively different from the cold dark matter scenario and more complex than originally assumed – a hybrid between top-down and bottom-up mechanisms. Moreover, warm dark matter halos contain visible caustic and shells with shallower density profiles, depending on the free streaming length of the particles. Predictions that can be tested by observations are given. Technical aspects of warm dark matter simulations are being discussed as well.