This is a survey of nilpotent orbits and representations in modular Lie algebras based on the work of J. C. Jantzen etc., and joint work with Bin Shu. We first recall the classical theory of nilpotent orbits in representations of reductive Lie algebras in prime characteristic. Then we further study nilpotent orbits of the Zassenhaus algebras, a class of Lie algebras of Cartan type. Different from the situation of reductive Lie algebras, there are infinitely many nilpotent orbits in the Zassenhaus algebras. All nilpotent orbits are precisely parameterized, and their dimensions are determined.