This talk proposes a Bayesian approach to regression with a tensor predictor or response. Tensor covariates/responses are commonly vectorized prior to analysis, failing to exploit the structure of the tensor, and resulting in poor estimation and predictive performance. We develop a novel class of multiway shrinkage priors for the coefficients in tensor regression models. Properties are described, including posterior consistency under mild conditions, and an efficient Markov chain Monte Carlo algorithm is developed for posterior computation. Simulation studies illustrate substantial gains over vectorizing or using existing tensor regression methods in terms of estimation and parameter inference. Detailed theoretical investigation of the proposed approaches will also be presented. The approach is illustrated using fMRI applications.