The process of nucleation and growth in glasses and undercooled liquids is modeled by directly simulating the evolution of the molecular cluster distribution under both isothermal and non-isothermal conditions. Results of that simulation for the nucleation rate during the quench, and for the number of nuclei produced and the volume fraction transformed at the end of the quench are presented. The following three points are discussed: (1) The importance of transient, or non-steady state, nucleation rates on glass formation is assessed by considering three model glass forming systems: lithium disilicate, a relatively good glass former, and two metallic glasses, (Au85Cu15)77Si9Gd14 and Au81Si19. (2) Using experimentally determined values for the steady state nucleation rates and growth velocities for Pd40Ni40P20, it is demonstrated that, in agreement with recent experimental results, this alloy may be cycled at rates on the order of 1 K/sec between the melting and glass transition temperatures without crystallization. Transient effects are shown to be unimportant under these conditions in this system. (3) The effect on glass formation of a non-equilibrium viscosity during the quench due to configurational freezing is evaluated by assuming a phenomenological model for the changing viscosity.