Next generation cellular network is expected to provide the simultaneous high-accuracy localization and ultra-reliable communication services, even in high mobility scenarios. To that end, the novel orthogonal time frequency space (OTFS) modulation has been developed as a promising physical-layer transmission technique, evident by the outstanding performance in terms of robustness against time-frequency selective fading over the orthogonal frequency division multiplexing (OFDM) counterpart. However, when OTFS meets massive multiple-input multiple-output (MIMO), the specific conditions, under which the delay-Doppler (DD) domain channel model holds, are not identified. In addition, the channel estimation and localization performance in such system is rarely studied. In this work, we target at these new challenges, and conduct comprehensive modelling, performance analysis, and algorithm design for massive MIMO-OTFS based simultaneous localization and communications. Specifically, we derive new channel models for the massive MIMO-OTFS system, which captures both time-frequency dispersion and spatial wideband effects. The specific conditions, under which the new models hold has been unveiled as well. Based on the new models, we establish the theoretical foundations for channel estimation and localization, by deriving the Cramer-Rao lower bounds of channel parameter and location estimation errors. Such bounds have been achieved with the newly designed low-complexity channel estimation and localization algorithms. Numerical simulations of the proposed framework with prevailing pulse functions are also conducted and the results validate the proposed designs and analysis. © 1983-2012 IEEE.