This package implements fast, scalable optimization algorithms for fitting topic models ("grade of membership" models) and non-negative matrix factorizations to count data. The methods exploit the special relationship between the multinomial topic model (also, "probabilistic latent semantic indexing") and Poisson non-negative matrix factorization. The package provides tools to compare, annotate and visualize model fits, including functions to efficiently create "structure plots" and identify key features in topics. The fastTopics package is a successor to the CountClust package. For more information, see <doi:10.48550/arXiv.2105.13440> and <doi:10.1186/s13059-023-03067-9>. Please also see the GitHub repository for additional vignettes not included in the package on CRAN.