In clinical trials, a placebo-controlled trial is common to demonstrate medical efficacy and safety/tolerability of the treatment of interest. However to demonstrate the treatment of interest is not worse than the already marketed treatment in the disease area, a non-inferiority trial can be appropriate. On the other hand, to demonstrate the similarity of the study treatment with other existing (already marketed) treatment, equivalence trials with clinical endpoints can be of interest. Challenges exist in selecting the non-inferiority or equivalence margin, in making the assumptions for variability estimate, in selecting the population, in the analyses, and in the interpretations of study results. This discussion will try to focus on some of these challenges and current statistical practices to handle those.