We address inference for a partially observed nonlinear non-Gaussian latent stochastic system comprised of interacting units. Each unit has a state, which may be discrete or continuous, scalar or vector valued. In biological applications, the state may represent a structured population or the abundances of a collection of species at a single location. Units can have spatial locations, allowing the description of spatially distributed interacting populations arising in ecology, epidemiology and elsewhere. We consider models where the collection of states is a latent Markov process, and a time series of noisy or incomplete measurements is made on each unit. A model of this form is called a spatiotemporal partially observed Markov process (SpatPOMP). The R package spatPomp provides an environment for implementing SpatPOMP models, analyzing data, and developing new inference approaches. We describe the spatPomp implementations of some methods with scaling properties suited to SpatPOMP models. We demonstrate the package on a simple Gaussian system and on a nontrivial epidemiological model for measles transmission within and between cities. We show how to construct user-specified SpatPOMP models within spatPomp.