Though the neutral kaon system has been studied for many years, it remains a rich hunting ground for the performance of incisive studies and for possible new discoveries. In this hunt, KTeV will be armed with an intense source of high-energy kaon decays together with a state-of-the-art detector capable of very high precision measurements. Our goal is to extract the value of the CP-violation parameter Re(epsilon'/epsilon) with an uncertainty of 1*10**-4, nearly an order of magnitude better than at present. We also aim to observe rare four-body KL decays with branching fractions as small as 10**-11, an improvement of two orders of magnitude over today's sensitivity.