Approaches to inference in a hierarchical generalized linear model depend on how the parameters are viewed. One approach assumes all parameters, except for the random effects, are fixed and unknown. The other approach assumes all parameters are random. In the former case, inference focuses on the likelihood while in the latter inference focuses on the posterior distribution of the parameters. Both the marginal likelihood and the Bayesian approaches require integration over many parameters, making analytical results unlikely and the computation intractable. As a result, various computational algorithms have been proposed. These approaches fall into three general categories: asymptotic approximations, numerical integration, and simulation-based integration methods. Asymptotic approximations generally do not perform well in high dimensions, and while some numerical integration approaches can handle high dimensions, they generally will not be suitable. In this chapter, asymptotic methods and numerical integration approaches are briefly reviewed but iterative simulation methods are the focus.