A notion of majorization for n-tuples of complex numbers plays an interesting role in a diverse collection of problems in linear algebra. When applied to the n-tuple eigenvalue lists of self-adjoint matrices, several fascinating operator theoretic results can be obtain. One example of this that has received much attention in recent years is the Schur-Horn Theorem, which classifies the possible diagonal n-tuples of a self-adjoint matrix based on its eigenvalues. In this talk, we will discuss the notion of majorization of self-adjoint operators in II_1 factors and its application. In particular, we will discuss the Schur-Horn Theorem in II_1 factors (due to Ravichandran), a classification of possible diagonals of operators in II_1 factors based on singular values (joint work with Matt Kennedy), and other applications of majorization in II_1 factors (joint work with Ken Dykema)