In this study we have considered different methods of estimation of the unknown parameters of a two-parameter Rayleigh distribution from both the frequentists' and the Bayesian view points. First, we briefly describe different frequentists' approaches: maximum likelihood estimators, method of moments estimators, L-moment estimators, percentile-based estimators, and least squares estimators, and we compare them using extensive numerical simulations. We have also considered Bayesian inferences of the unknown parameters. It is observed that the Bayes estimates and the associated credible intervals cannot be obtained in explicit forms, and we have suggested using an importance sampling technique to compute the Bayes estimates and the associated credible intervals. We analyze one dataset for illustrative purposes.