PPP methods for tomographic imaging are presented in this chapter. The primary emphasis is on methods for emission tomography, but transmission tomography is also included. The famous Shepp-Vardi algorithm for positron emission tomography (PET) is obtained via the EM method for time-of-flight data. Single-photon emission computed tomography (SPECT) is used in practice much more often than PET. It differs from PET in many ways, yet the models and the mathematics of the two methods are similar. (Both PET and SPECT are also closely related to multitarget tracking problems discussed in Chapter 6.) Transmission tomography is the final topic discussed. The Lange-Carson algorithm is derived via the EM method. CRBs for unbiased estimators for emission and transmission tomography are discussed. Regularization and Grenander’s method of sieves are reviewed in the last section.