In this paper, the classical and Bayesian estimators of the unknown parameters and the reliability function of the inverse Weibull distribution are considered. The maximum likelihood estimators (MLEs) and modified maximum likelihood estimators (MMLEs) are used in the classical parameter estimation. Bayesian estimators of the parameters are obtained by using symmetric and asymmetric loss functions under informative and non-informative priors. Bayesian computations are derived by using Lindley approximation and Markov chain Monte Carlo (MCMC) methods. The asymptotic confidence intervals are constructed based on the maximum likelihood estimators. The Bayesian credible intervals of the parameters are obtained by using the MCMC method. Furthermore, the performances of these estimation methods are compared concerning their biases and mean square errors through a simulation study. It is seen that the Bayes estimators perform better than the classical estimators. Finally, two real-life examples are given for illustrative purposes.