As a non-parametric method, Empirical Likelihood (EL) has been attracting seriousattention from researchers in statistics, econometrics, engineering and biostatistics. Bydefining the estimation equations in EL appropriately, we can extend EL to various datasettings, especially those in which parametric likelihoods are absent. In this dissertation,two applications of empirical likelihood are explored: quantile estimation and longitudinaldata analysis. Quantile estimation for discrete data analysis has not been well studied. Fora given 0 < p < 1, the commonly used sample quantile may or may not be consistent for thepth quantile, depending on whether or not the underlying distribution has a plateau at thelevel of p. I propose an EL-based categorization procedure which not only helps determinethe shape of the true distribution at level p, but also provides a way of formulating a newestimator that is consistent in any case. For non-Gaussian longitudinal data, generalized estimatingequations (GEE) are a popular class of marginal models. While the GEE estimatoris consistent and robust, it may suffer significant loss of efficiency if the working correlationstructure is misspecified. I consider the use of EL to select working correlations for GEEmodels, for which parametric likelihoods are absent and quasi-likelihoods are difficult toconstruct.