This paper summarizes, defines, and discusses multiple endpoints comparison procedures, concepts, and methodologies for applications to clinical trials. We address the more widely used methods of alpha-level, p-value, and critical value adjustments. We examine global assessment measures such as O'Brien's test and Simes' procedure and contrast them with the alpha-adjustment procedures of Bonferroni and Holm. We propose a global assessment procedure based on categorization of the individual endpoints to form an overall composite endpoint. Additionally, we discuss a new weighting scheme for Holm's sequentially rejective alpha-adjustment procedure. Investigation of the correlation between endpoints is examined in relation to adjustment of the alpha-level. In the context of a clinical trial, the above multiplicity procedures are applied and compared. Finally, some comments concerning ease of use and relevance are summarized for the above methods.