Warm dark matter models are a viable alternative to the cold dark matter models challenged by many recent observations (e.g. dwarf galaxies, pure-disk galaxies, matter distribution in voids) and by the narrowed detection limits. I will review some theoretical assumptions made in describing the properties and behavior of different WDM candidates (in a wide mass range) and discuss the constraints from simulation results in the astrophysical contexts at both large and small scales.The intrinsic properties of WDM particles, strongly dependent on the assumed particle model and production mechanism, imprint a distinct signature on the structure formation and evolution. Using N-body cosmological simulations I will show that the structure formation mechanism in WDM is qualitatively different than in the CDM scenario and more complex than originally assumed - a 'hybrid' between 'top-down' and 'bottom-up' clustering on multiple scales - depending locally on the morphology of the analyzed region and globally on the free streaming length of the simulated particle. On smaller scales, the properties of WDM particles influence the shape and outlook of halos - caustics and shells and their internal structure - density and phase space density profiles. I will also comment on the technical aspects in simulating WDM and describe possible observational tests for distinguishing between dark matter models.