Modern statistical methods, in particular Bayesian hierarchical models, provide a framework for combining various types of measurements in a single analysis. I'll describe a basic latent variable framework for dealing with spatial and spatio-temporal data. The approach is to represent the spatial and spatio-temporal field of interest as a latent field and relate observations to that field. An observation may represent a single point in space and time or an average over space and time. Then I'll describe how to use the approach to combine measurements with proxies such as computer code (model) output and remote sensing output. A critical aspect in many applications is accounting for systematic discrepancy between the proxy and the latent, unknown true field. I'll present a case study of modeling ambient particulate matter in the eastern U.S. Finally, I'll briefly discuss other methods in the statistical literature for combining measurements and model output and accounting for discrepancy.