There are currently three main approaches to parameter estimation in item response theory (IRT): (1) joint maximum likelihood, exemplified by LOGIST, yielding maximum likelihood estimates; (2) marginal maximum likelihood, exemplified by BILOG, yielding maximum likelihood estimates of item parameters (ability parameters can be estimated subsequently, using Bayesian procedures); and (3) Bayesian approaches--parameter estimates are usually the mode or mean of the posterior distribution of the parameter estimated. Advantages and disadvantages of these three methods are discussed and compared. (Author/BW)