In this work, we present and discuss recent results of analytical investigations of black hole (BH) shadow. First of all, we discuss definition of shadow in details. Then, we describe fully analytical approach for extraction of spin of BH from the deformation of its shadow. Finally, we present analytical investigation of plasma influence on the shadow size. This paper is based on talk given at the conference ‘High-Energy Phenomena in Relativistic Outflows VI', September 11–15, 2017, Moscow, Russia.