Larger amounts of spatial or spatiotemporal data with more complex structures collected at irregularly spaced sampling locations are prevalent in a wide range of disciplines. With few exceptions, however, practical statistical methods for nonlinear modeling and analysis of such data remain elusive. In this talk, I provide a review on some developments and progress of the research that my co-authors and I have recently done. In particular, we will look at some nonparametric methods for probability, including joint, density estimation, and semiparametric models for a class of spatio-temporal autoregressive partially nonlinear regression models permitting possibly nonlinear relationships between responses and covariates. In the setting of semiparametric spatiotemporal modelling, I will also show a computationally feasible data-driven method for spatial weight matrix estimation. For illustration, our methodology is applied to investigate some land and housing prices data sets.