Abstract: Conformal properties of spacetime are important in any theory of gravitation including string theories and their reductions. Within the classical Einstein theory the concept of conformal compactification allows to study the global structure of spacetime in a convenient way. In this talk I focus on asymptotically flat spacetimes as models for isolated systems which can emitt the gravitational radiation. In this case the conformal approach is related to the more traditional description of gravitational waves of Bondi and Sachs. The Penrose (conformal) approach allows to express in a geometric way restrictions on spacetime metric which guarantee that it looks like Minkowski metric at large distances from the source. In a sense the "infinity" is brought into a finite region, so-called 'scri', on which one can study the outgoing gravitational radiation and overall characteristics of the system like energy and momentum. Suprisingly the symmetry group of the scri, the BMS group, is bigger than the Poincare group. Due to this fact there are difficulties, and also different possibilities, in defining the total angular momentum of the system. Up to date there is no satisfactory exact solution of the Einstein equations which would represent gravitational radiation of a spatially bounded source. Perhaps such solutions can be found among algebraically special metrics which are related to the Cauchy-Riemann structures.