In this book, we address the issue of gravitational collapse in electromagnetic theory. For this purpose, we adopt two approaches one by assuming charged perfect fluid in the interior of a star and another by studying the dynamics of thin shell of matter on the surface of a charged star. The cylindrically symmetric charged perfect fluid collapse is explored by assuming that charged perfect fluid is moving along geodesics in the interior of cylinder. In this case, the analytic solution of the Einstein-Maxwell field equations represents gravitational collapse. The end state of collapse is found to be conical singularity. We formulate general dynamical equations using Israel thin shell formalism in charged background which helps to investigate gravitational collapse of scalar field and polytropic matter thin shell. In massless case, we find that scalar shell either expands to infinity or collapses to a point forming a curvature singularity. Also, the massive scalar field shell can exhibit the bouncing behavior. It is found that expanding and collapsing polytropic matter as well as perfect fluid shell comes to rest, then re-expands to infinity or re-collapses to a point.