Estimation of ability and item parameters in latent trait models is discussed. When both ability and item parameters are considered fixed but unknown, the method of maximum likelihood for the logistic or probit models is well known. Discussed are techniques for estimating ability and item parameters when the ability parameters or item parameters are considered random. When the item parameters are considered fixed, and the ability parameters are random, from some prior distribution with fixed but unknown parameters, the EM algorithm is applied. A modification of the EM algorithm, which requires considerably less computation, is proposed. When both ability and item parameters are considered random, the EM algorithm seems to be impractical because the amount of computation needed is very large. In this case another modification to the EM algorithm is proposed. One advantage to using prior distributions is that parameter estimates usually exist in situations where the maximum likelihood estimates do not. These methods are applied to the one parameter logistic (Rasch) model and numerically compared using several sets of simulated data. It appears likely that most of the methods discussed here can be readily extended to the two and three parameter logistic or probit model. (Author/GK)