Random matrix theory is a field with applications in physics, statistics, and number theory. All math students have worked with matrices whose entries are constant, but when these entries are random, new tools and techniques have been developed to study the properties of the matrix. The limiting eigenvalue distribution of random matrices is of particular interest, and many results describe this distribution for specific random matrices. In my senior thesis, I study what happens to the limiting eigenvalue distribution of a random matrix when some entries of the matrix are changed to zero in random and non-random ways. In general, I show that if “not too many” entries are changed to zero, then the limiting eigenvalue distribution is unchanged. If many zero distortions are added, then the location of these zeros in the matrix can influence the limiting eigenvalue distribution.