Microscopic calculations of Compton scattering on the free proton and light nuclei are presented. For the description of Compton scattering on the proton the conventional K-matrix approach and the ``Dressed K-Matrix'' model are introduced. The latter approach can be used to calculate polarizabilities as well as Compton scattering for photon energies upto 1 GeV since it obeys the symmetry properties which are appropriate in the different energy regions. In particular, crossing symmetry, gauge invariance and unitarity are satisfied. The extent of violation of analyticity (causality) is used as an expansion parameter. Coherent Compton scattering on light nuclei at 200--300 MeV is studied in the impulse approximation and is shown to be a sensitive probe of the in-medium properties of the \Delta -resonance. Modifications of the properties of the \Delta-resonance due to the nuclear medium are accounted for through the self-energy operator of the \Delta. The dominant medium effects such as the Pauli blocking effects in the decay width, effective nucleon mass and particle--hole excitations in the pion propagator are consistently included in nuclear matter.