In this article we review the image reconstruction algorithms used in tomography. We restrict ourselves to the standard problems in the reconstruction of function from line or plane integrals as they occur in X-ray tomography, nuclear medicine, magnetic resonance imaging, and electron microscopy. Non-standard situations, such as incomplete data, unknown orientations, local tomography, discrete tomography are not dealt with. Nor do we treat nonlinear tomographic techniques such as impedance, ultrasound, and near infrared imaging.