A microscopic statistical dynamical theory for the effect of deformation on the transient localization, shear modulus, relaxation time, viscosity and other dynamic properties of glassy colloidal suspensions and entropic depletion gels has been developed. The approach is built on single particle activated barrier hopping on a nonequilibrium free energy profile as the elementary physical process in quiescent systems. External deformation distorts the confining free energy, weakens the caging constraints, and accelerates dynamics. The roles of mechanically driven motion and thermally activated flow have been studied. For glassy hard sphere suspensions power law and/or exponential dependences of the modulus and yield stress on colloid volume fraction are predicted. For polymer-particle suspensions the caging constraints and physical bond strength are quantified using PRISM integral equation theory. The absolute yield stress collapses onto a universal master curve as a function of polymer concentration when scaled by its value at the ideal mode-coupling theory nonergodicity transition, and sufficiently deep in the gel is of a power-law form with a universal exponent. The volume fraction dependence also exhibits such scaling but with a nonuniversal exponent. The theory has also been applied to thermal gels composed of colloids with sticky brush layers. Generalization of the approach to suspensions of nonspherical colloidal molecules has been initiated. Distinctive changes in the location of ideal glass and gel boundaries, barriers and yield stresses with particle shape are found. This work was done in collaboration with Y.L.Chen. V.Kobelev, E.J.Saltzman and G.Yatsenko.