Reliability assessment of engineered structures is a powerful and useful concept to estimate the structural capacity of withstanding hazardous events during their service lives. Taking into account the time variation of both structural resistance and the external load processes, the structural safety level is dependent on the duration of service period of interest, due to the accumulation of hazards by exposure in time. This paper presents an overview on the nonempirical assessment methods for time-dependent reliability of deteriorating structures. Generally, these methods can be classified into two types, namely simulation-based and analytical methods. The former is usually brute, and is especially suitable for solving high-dimensional reliability problems. Conversely, analytical solutions may improve the calculation efficiency significantly, and offer insights into the reliability problem that otherwise could be difficult to achieve through Monte Carlo simulation. Both the simulation