State-of-the-art technologies for VLSI circuits give rise to various defect mechanisms that may cause a circuit to fail when operated at its designated speed of operation. Such defects are conventionally modeled by delay faults. In this paper, we review delay fault models used for circuits described at the gate level. The shortcomings of these models in accommodating physical phenomena that determine the worst-case delay of a circuit, and in modeling physical defects, were described in several works. We review methods proposed recently to address these shortcomings at the gate level, and describe a new approach based on a generalized fault model. This model requires that several tests be used for each fault to encompass the conditions leading to the worst-case delay associated with the fault, thus alleviating the need for accurate modeling of these conditions. Functional delay fault models were also proposed to address several of the shortcomings of gate-level models. We review these models and discuss their advantages and disadvantages. Throughout this paper, we also review test generation procedures for delay faults, and present experimental results of these procedures where appropriate.