Understanding the origin of hierarchies is one of the main driving forces of today's fundamental research. The well-known examples are provided by the hierarchy between the weak and Planck scales, the hierarchy between neutrino and electron masses and the hierarchy between the Planck scale and the vacuum energy of the present Universe. Sometimes these puzzles are classified as so-called ``naturalness problems". Historically, in the case of proton/pion mass hierarchy, such questions led to advances that changed modern particle physics. In this talk we review certain representative examples when the hierarchy can be taken as a serious indication for new physics. We also review cases when a seeming naturalness problem is nullified by consistency of the theory. We give an example of the celebrated naturalness puzzle of the cosmological term. This however turns out to be fictitious, since the consistency of the S-matrix formulation demands that the cosmological constant is excluded from the energy budget of our Universe.