Nonlocal operators have attracted great attention in the last decades due to their ability to model phenomena in which long range interaction occurs. In this talk, we shall be interested in special types of nonlocal operators, namely the fractional powers of the Laplace operator. In the first part, we shall briefly discuss how these operators appear in fields such as probability. In the second part we investigate the so-called Pohozaev-type identities for these operators and discuss their applications, especially in non-existence results for equations with supercritical nonlinearities.