The understanding and the complete description of the glass transition are impeded by the complexity of nature of the glass. Parts of this complexity come from the emergence of long-lived inherent structures of a liquid at a temperature below which the activated reconfiguration events play a dominant role. Molecules in a glass change their locations through the activated process at a rate which varies throughout the glass owing to these local and aperiodic structures. Motions in one location also cause or relieve constrains, thereby altering the rate of transitions of neighboring regions. The key to understanding this problem is the interplay between the activated events that generate mobility and the transport of mobility. In the following we explore fluctuating mobility generation and transport in glasses to understand the dynamics of the glassy state within the framework of the random first order transition theory of glass. Fluctuating mobility generation and transport in the glass that arise from there being a distribution of local stability and thus effective temperature are treated by numerically solving stochastic continuum equations for mobility and fictive temperature fields. Fluctuating spatiotemporal structures in aging and rejuvenating glasses lead to dynamical heterogeneity in glasses with characteristics that are distinct from those found in the equilibrium liquid. We illustrate in this thesis how the heterogeneity in glasses gives rises of a non-Gaussian distribution of activation free energies, the stretching exponent, and the growth of characteristic lengths. These are studied along with the four-point dynamic correlation function. Asymmetric thermodynamic responses upon heating and cooling are also predicted to be the results of the heterogeneity and the out-of-equilibrium behavior of glasses below the glass transition temperature. Moreover the dynamical heterogeneity can lead to a growth front of mobility in rejuvenating glasses that emanates from the surface where stable glasses are heated. Noticeably bimodal distributions of local fictive temperatures in aging glasses are also investigate. This result explains recent experimental observations that have been interpreted as coming from these being two distinct equilibration mechanisms in glasses.

Finally we study the mechanical properties of glasses. The remarkable strength of glasses is examined using the random first order transition theory. The theory predicts that the strength not only depends on the elastic modulus but also depends on the amount of configurational energy frozen in when the glass is prepared. The stress catalysis of cooperative rearrangements of the same type as those responsible for the supercooled liquid's high viscosity account quantitatively for the measured strength of a range of metallic glasses, silica and a polymer glass.