Abstract: In this talk we'll be covering some work by Sandeep Varma concerning rational submonoids of algebraic monoids. We begin by reviewing the Bruhat decomposition for algebraic groups, as discovered by Francois Bruhat. From there we'll take two different paths, the first will generalize the Bruhat decomposition to groups with BN-pairs. The second will deal with the Bruhat decomposition for algebraic monoids. Finally we will cover the results from Varma's paper which culminate in extending the Bruhat decomposition to rational submonoids.