Pyrat Bay computes radiative-transfer spectra and fits exoplanet atmospheric properties, and is an efficient, user-friendly Python tool. The package offers transmission or emission spectra of exoplanet transit or eclipses respectively and forward-model or retrieval calculations. The radiative-transfer includes opacity sources from line-by-line molecular absorption, collision-induced absorption, Rayleigh scattering absorption, and more, including Gray aerosol opacities. Pyrat Bay's Bayesian (MCMC) posterior sampling of atmospheric parameters includes molecular abundances, temperature profile, pressure-radius, and Rayleigh and cloud properties.