Two proposed likelihood models for emission and transmission image reconstruction accurately incorporate the Poisson nature of photon counting noise and a number of other relevant physical features. As in most algebraic schemes, the region to be reconstructed is divided into small pixels. For each pixel a concentration or attenuation coefficient must be estimated. In the maximum likelihood approach these parameters are estimated by maximizing the likelihood (probability of the observations). EM algorithms are iterative techniques for finding maximum likelihood estimates. In this paper we discuss the general principles behind all EM algorithms and derive in detail the specific algorithms for emission and transmission tomography. The virtues of the EM algorithms include (a) accurate incorporation of a good physical model, (b) automatic inclusion of non-negativity constraints on all parameters, (c) an excellent measure of the quality of a reconstruction, and (d) global convergence to a single vector of parameter estimates. We discuss the specification of necessary physical features such as source and detector geometries. Actual reconstructions are deferred to a later time.