The Kervaire Invariant is an invariant of 4n+2 dimensional manifolds which measures the similarities between a manifold and a sphere of the same dimension. The Kervaire Invariant problem concerns the Kervaire Invariant of all manifolds of a given dimension, and has been solved in every dimension save for 126. We will begin with an accessible description of the Kervaire Invariant and the Kervaire Invariant problem, and then discuss the Kervaire Invariant problem from the perspective of algebraic topology and homotopy theory.