Superiority trials are designed to test the hypothesis that a given diagnostic or therapeutic strategy is better than (i.e. "superior to") placebo or an active control. Conversely, non-inferiority trials test the hypothesis that a newer (i.e. alternative) strategy is not "unacceptably worse" than a control (i.e. "traditional", or "older") strategy. Non-inferiority trials are increasingly conducted in clinical medicine more often when a "newer" strategy is supposed to offer a relevant advantage in terms other than clinical efficacy (i.e. better tolerability, less cost, simpler regimen, etc.) versus a "gold standard" traditional strategy. The principle underlying non-inferiority trials is that the above advantage justifies the preferential use of the newer strategy in the clinical practice even if the clinical efficacy of the "new" appears to be a bit worse than that of the "old", albeit not unacceptably worse (i.e. not beyond a pre-specified value). The demonstration of non-inferiority requires that the confidence interval of the point estimate (e.g. the hazard ratio) does not cross a pre-specified limit. The definition of such pre-specified limit, the so called "non-inferiority margin", is a pivotal point when planning non-inferiority trials. It denotes the maximally tolerated worse effect of the alternative strategy, compared with the traditional one, required to conclude that an alternative strategy is non-inferior to the traditional "gold standard". The non-inferiority margin is derived from previous trials evaluating the efficacy of the traditional strategy vs placebo. We reviewed the principles and the practical aspects in the design and conduct of non-inferiority trials.