Layered structures of the high Tc superconductors have reinstigated the study of two dimensional (2D) antiferromagnetic spin systems and their charge dynamics for more than a couple of decades now. As a hole moves through such a system it interacts with spin waves and phonons at finite temperature. This book contains systematic derivation of the hole spectral functions in a 2D t-J model and its extensions numerically by first finding the spin waves using linear spin wave approximation and then solving the hole Dyson's equation within the Non-crossing approximation. The role of different parameters and scenario on the hole dynamics in such a system is investigated in detail. Particularly the three main chapters in this book deals with hole dynamics (i) when optical phonons are present in the system at finite temperature, (ii) when small but finite hole density is present in the system and (iii) when periodic antiferromagnetic domain walls are present. This book shows computational results extrapolated to thermodynamic limit and its comparison with the angle-resolved-photo-emission spectra of the high Tc Cuprates in order to understand some aspects of charge flow in such compounds.