In this survey paper, we begin with a brief history of the celebrated Belousov-Zhabotinskii (BZ) reaction. In particular, we consider the BZ reaction in a continuously stirred, closed vessel in the presence of a ferroin indicator. We examine the underlying chemical kinetics of the most significant reactions involved. This leads to the Oregonator model and an associated 3 x 3 system of nonlinear ordinary differential equations. We nondimensionalize this system and further reduce it to a 2 x 2 stiff system. Relaxation oscillations are expected and an analysis of the phase plane confirms this. Finally, we solve the system numerically for a certain set of system parameters and compare our computations with experimental results.