Highest weight categories are useful for studying the derived category of a nonsemisimple abelian category. They were introduced after developments for the BGG category O and modular representations of symmetric groups. I will recall and advertise this notion and show that certain natural representations of Borel subalgebras for classical Lie algebras and the Lie superalgebra osp(1|2n) admit a highest weight structure. Advisor: Dr. Maxim Gurevich