We have defined four categories of algorithms for reconstructing objects from their projections: summation methods (tomography)l use of Fourier Transforms; analytic solution of the integral equations; and series expansion approaches. An example of each has been developed in detail. In our discussion we have noted: 1. All methods yield only estimates of the original structure. 2. There is no theoretical framework that can predict the relative performance of algorithms under all conditions encountered in practical applications. Hence algorithms must be compared using test patterns or phantoms and modes of data collection typical of one's applications. 3. Reconstruction from projections encompasses a vast range of applications. For this reason there has been considerable research duplication.