Point spread function (PSF) models are critical to Hubble Space Telescope (HST) data analysis. Astronomers unfamiliar with optical simulation techniques need access to PSF models that properly match the conditions of their observations, so any HST modeling software needs to be both easy-to-use and have detailed information on the telescope and instruments. The Tiny Tim PSF simulation software package has been the standard HST modeling software since its release in early 1992. We discuss the evolution of Tiny Tim over the years as new instruments and optical properties have been incorporated. We also demonstrate how Tiny Tim PSF models have been used for HST data analysis. Tiny Tim is freely available from tinytim.stsci.edu.