In this thesis, I have considered the scenario of the accretion of phantom energy onto various types of black holes. The phantom energy is a strange kind of energy existing in the universe that drives the cosmic accelerated expansion. Among various black holes, we have chosen the following for our study: Schwarzschild, Riessner-Nordstrom, primordial and BTZ black holes. I also discuss various possibilities of phantom energy as viscous Chaplygin gas and modified variable Chaplygin gas.