Estimating the rate of molecular evolution over time is crucial for understanding the processes and forces that shape biological diversity. To this end, viruses are particularly useful study organisms because they evolve much more quickly than cellular organisms. For example, the rates of evolution of influenza viruses are up to six orders of magnitude higher than those of mitochondrial DNA in vertebrates. This is one of the main explanations for the large proportion of infectious diseases caused by viruses. Having high rates of evolution allows viruses to evade the immune response of their hosts and to infect different host species. Accurate estimates of rates of evolution are also necessary for inferring evolutionary timescales, which provide information about the emergence and long-term evolution of viruses. However, estimating rates of evolution is a challenging task that requires different statistical and computational tools. I will present a set of studies dealing with rates of evolution and the estimation of evolutionary timescales in viruses. Analyses of empirical data demonstrate the effect of natural selection and mutational saturation on viral rates of evolution. In particular, there is a time-dependen pattern in rate estimates, which is sustained across different groups of viruses. Finally, I will discuss computational tools to improve the accuracy and precision of estimates of evolutionary rates timescales in viruses and other microorganisms.