The solid state properties of polyolefins are exquisitely sensitive to the molecular structure and chain-like nature of the molecules and to the organization of these chains into the semicrystalline morphology. These properties reflect both the kinetic nature of the crystallization phenomenon and the thermodynamic behavior of the resulting crystal/amorphous polymer composite. Description and modeling of polyolefin crystallization and semicrystalline solid properties with atomic level detail pose significant challenges for molecular simulation, due to the nonequilibrium nature of the structures and the broad spectrum of time scales involved with structural reorganization. Here we describe progress in the development of molecular simulations to illuminate these phenomena. Particular emphasis is placed on the nonequilibrium nature of the semicrystalline morphology and the consequences this holds for modeling the structure and mechanical properties of this material. The crystallization in polymers is characterized by rare event dynamics that control both the nucleation and growth of the crystal domains from the melt phase.  Efforts to study these phenomena in short chain olefins, with potential for extension to longer chains and melts with flow-induced orientation, may also be discussed.