Survival methods are used for the statistical modelling of time-to-event data, with applications in many scientific fields. Survival data are characterised by a set of complete records, in which the time of the event is known; and a set of censored records, in which the event was known to have occurred in an interval. When survival data are spatially referenced, the spatial variation in survival times may be of scientific interest. In this article, we introduce a new R package, spatsurv, for inference with spatially referenced survival data. The specific type of model fitted by this package is a parametric proportional hazards model in which the spatially correlated frailties are modelled by a log-Gaussian stochastic process. The package is extensible in that it allows the user to easily create new models for the baseline hazard function and spatial covariance function. The package implements an advanced adaptive Markov chain Monte Carlo algorithm to deliver Bayesian inference with minimal input from the user.