fixest is an R package for fast and flexible econometric estimation, providing a comprehensive toolkit for applied researchers. The package particularly excels at fixed-effects estimation, supported by a novel fixed-point acceleration algorithm implemented in C++. This algorithm achieves rapid convergence across a broad class of data contexts and further enables estimation of complex models, including those with varying slopes, in a highly efficient manner. Beyond computational speed, fixest provides a unified syntax for a wide variety of models: ordinary least squares, instrumental variables, generalized linear models, maximum likelihood, and difference-in-differences estimators. An expressive formula interface enables multiple estimations, stepwise regressions, and variable interpolation in a single call, while users can make on-the-fly inference adjustments using a variety of built-in robust standard errors. Finally, fixest provides methods for publication-ready regression tables and coefficient plots. Benchmarks against leading alternatives in R, Python, and Julia demonstrate best-in-class performance, and the paper includes many worked examples illustrating the core functionality.