CLOUDY is a large-scale spectral synthesis code designed to simulate fully physical conditions within an astronomical plasma and then predict the emitted spectrum. Here we describe version 90 (C90) of the code, paying particular attention to changes in the atomic database and numerical methods that have affected predictions since the last publicly available version, C84. The computational methods and uncertainties are outlined together with the direction future development will take. The code is freely available and is widely used in the analysis and interpretation of emission-line spectra. Web access to the Fortran source for CLOUDY, its documentation Hazy, and an independent electronic form of the atomic database is also described.