Subordinators is a class of stochastic process with non-decreasing paths and stationary and independent increments, so they are non-decreasing Lévy processes.Subordinators are relevant in various areas of theoretical and applied probability, in particular they allow for a better understanding of more general Lévy processes via the so called Wiener-Hopf factorization and its pathwise explanation. The fact of having non-decreasing paths makes them more easy to handle in several aspects but there are some properties that are not so well understood, as for instance explicit formulas for their distribution function. In this talk, I will speak about some areas where subordinators are relevant and I will describe some recent results on the behavior of the first passage time or inverse process, that are rather precise and allow for some explicit computations.