FitTeD solves time-dependent general relativistic disc equations to fit multi-band light curves and spectra. It includes relativistic optics effects such as Doppler and gravitational energy shifting, and gravitational lensing, and can include non-disc light curve and spectral components to, for example, model the early time rise and decay of tidal disruption event light curves in optical-to-UV bands. FitTeD also provides Monte Carlo Markov Chain fitting procedures that return posterior distributions of black hole and disc parameters.