This presentation is centered on hierarchical modeling for problems in spatial and spatio-temporal statistics.  It draws its motivation from current and recent interdisciplinary research work I have been involved with in terms of applications in the environmental sciences - ecological processes, environmental exposure, and weather modeling.  I will briefly review hierarchical modeling specifications, adopting a Bayesian perspective with full inference and associated uncertainty within the specification, while acieving exact inference to avoid what may be uncomfortable asymptotics.  I will focus on point-referenced (geo-statistical) and point pattern spatial settings.  I will consider in some detail problems involving data fusion, species distributions, and large spatial datasets.  Also, I will briefly describe four further examples involving Bayesian nonparametrics and spatial modeling, space time kernel averaged predictiors for distributed lags in space and time, spatial processes built for directional data using Gaussian processes, and space-time analysis of extreme value data.