Signatures of glassy dynamics have been identified experimentally for a rich variety of materials in which molecular networks provide rigidity. Here we present a theoretical framework to study the glassy behavior of both passive and active network materials. We construct a general microscopic network model that incorporates nonlinear elasticity of individual filaments and steric constraints due to crowding. Based on constructive analogies between structural glass forming liquids and random field Ising magnets implemented using a heterogeneous self-consistent phonon method, our scheme provides a microscopic approach to determine the mismatch surface tension and the configurational entropy, which compete in determining the barrier for structural rearrangements within the random first order transition theory of escape from a local energy minimum. The influence of crosslinking on the fragility of inorganic network glass formers is recapitulated by the model. For active network materials, the mapping, which correlates the glassy characteristics to the network architecture and properties of nonequilibrium motor processes, is shown to capture several key experimental observations on the cytoskeleton of living cells: Highly connected tense networks behave as strong glass formers; intense motor action promotes reconfiguration. The fact that our model assuming a negative motor susceptibility predicts the latter suggests that on average the motorized processes in living cells do resist the imposed mechanical load. Our calculations also identify a spinodal point where simultaneously the mismatch penalty vanishes and the mechanical stability of amorphous packing disappears.