Implementation of uniformity tests on the circle and (hyper)sphere. The main function of the package is unif_test(), which conveniently collects more than 35 tests for assessing uniformity on S^p-1 = x in R^p : ||x|| = 1, p >= 2. The test statistics are implemented in the unif_stat() function, which allows computing several statistics for different samples within a single call, thus facilitating Monte Carlo experiments. Furthermore, the unif_stat_MC() function allows parallelizing them in a simple way. The asymptotic null distributions of the statistics are available through the function unif_stat_distr(). The core of sphunif is coded in C++ by relying on the Rcpp package. The package also provides several novel datasets and gives the replicability for the data applications/simulations in Garcà a-Portugués et al. (2021) <doi:10.1007/978-3-030-69944-4_12>, Garcà a-Portugués et al. (2023) <doi:10.3150/21-BEJ1454>, Garcà a-Portugués et al. (2024) <doi:10.48550/arXiv.2108.09874>, and Fernández-de-Marcos and Garcà a-Portugués (2024) <doi:10.48550/arXiv.2405.13531>.