We describe the main theoretical principles behind Time-resolved Optical Absorption and Scattering Tomography (TOAST). The problem is viewed as the optimisation of an error-norm derived from correlated statistics of the time-dependent photon intensity at the surface of an object. The field is compared with Electrical Impedance Tomography (EIT). Some inverse algorithms are suggested and one implemented in detail: a modified Newton-Raphson approach. Several regularisation schemes are described. Results are given for these schemes applied to several different data sets.