Stationarity is a fundamental notion of dependence that underlies many developments in spatial statistics. However, global stationarity is usually too stringent for applications. In this talk, we introduce a notion of local stationarity that is satisfied by a large class of nonstationary processes, including multifractional Brownian motions and deformation processes. We develop an inferential approach for the locally stationary process based on dense spatial data and consider its asymptotic theory.