In section 2 we describe the most important algorithm in tomography, namely the filtered backprojection algorithm. It not only is the working horse for present day's tomography, but also serves as model for the algorithms in future imaging devices such as the 3D algorithms described in section 3. Since many imaging problems can be described by large linear sparse systems of equations iterative methods suggest themselves, see section 4. Algorithms exploiting rotational symmetry of the imaging devices are described in section 5. In section 6 we deal with algorithms which work exclusively in Fourier space and which have the potential to outperform the filtered backprojection algorithm in speed.