An important characteristic of many engineering systems is that they behave dynamically, i.e. their response to an initial perturbation evolves over time as system components interact with each other and with the environment. Conventional event tree/fault tree methods for risk assessment are designed to illustrate static relationships between logical variables, and do not explicitly treat time, process variables, or human behavior (which affect the system dynamic response). This paper discusses the motivation for improved methods for dynamic system analysis, and provides an overview of a number of alternative methodologies. The alternative methodologies reviewed include extensions of the event tree/fault tree methodology (e.g. digraph-based methods), explicit state-transition methods (e.g. explicit Markov chain models), and implicit state-transition approaches (e.g. DYLAM, discrete event simulation). The ability of each methodology to deal with a simple example problem and with human behavior issues is discussed. It is shown that, while all of the methodologies are useful for different levels of dynamic analysis, implicit approaches have significant representational as well as computational advantages when treating large, highly complex systems.