Summary: We present the PyMOSO software package for (1) solving multiobjective simulation optimization (MOSO) problems on integer lattices and (2) implementing and testing new simulation optimization (SO) algorithms. First, for solving MOSO problems on integer lattices, PyMOSO implements R-PERLE, a state-of-the-art algorithm for two objectives, and R-MinRLE, a competitive benchmark algorithm for three or more objectives. Both algorithms use pseudogradients, are designed for sampling efficiency, and return solutions that, under appropriate regularity conditions, provably converge to a local efficient set with probability 1 as the simulation budget increases. PyMOSO can interface with existing simulation software and can obtain simulation replications in parallel. Second, for implementing and testing new SO algorithms, PyMOSO includes pseudorandom number stream management, implements algorithm testing with independent pseudorandom number streams run in parallel, and computes the performance of algorithms with user-defined metrics. For convenience, we also include an implementation of R-SPLINE for problems with one objective. The PyMOSO source code is available under a permissive open-source license. The online supplement is available at \url{https://doi.org/10.1287/ijoc.2019.0902}.