Plücker coordinates arise as homogeneous coordinates for Grassmannians and flag varieties. They can be organized into the Plücker algebra, which can be viewed as the quotient of a polynomial algebra by the ideal of Plücker relations. We will introduce the definitions and applications of the Gröbner bases and sagbi bases. We will then find a Gröbner basis for the ideal of Plücker relations and a sagbi basis for the Plücker algebra. Finally, we discuss results that follow from the bases we found and make connections to the combinatorics of representations of GL_n(C). Speaker(s): Dawei Shen (UM)