Non-inferiority and equivalence trials aim to promote new treatments that are not expected to be superior to existing ones in a given indication. In order to compensate for a possible loss of efficacy, the new treatment should offer other advantages compared to the reference treatment, a better safety of use for example. Their methods somewhat differ from those of superiority trials, often better known to the medical community. This article presents the key points of the methodology of non-inferiority and equivalence trials in order to inform the readers of such trials about the issues and critical points. The general methodology (hypotheses, decision rules, number of subjects required, and strategy of analysis) is presented using examples and graphic illustrations. The issues and critical points are identified and discussed, in particular the choice of the comparator and of the margin of non-inferiority.