Brown-Gitler spectra have many uses in homotopy theory, largely due to the fact that they realize finite pieces of the dual Steenrod algebra, which is a key input for computing stable homotopy. However, Brown-Gitler spectra were not originally constructed with homotopical applications in mind. Instead, Brown and Gitler first constructed these spectra to aid in studying the immersion conjecture for differentiable manifolds. This talk will provide an overview of homotopical and geometric motivations for constructing Brown-Gitler spectra. We will describe four different constructions due to a range of authors, and discuss how these Brown-Gitler spectra are used in homotopy computations. These descriptions will motivate a sketch of current research directions in equivariant and motivic homotopy theory, and culminate in a statement of new results from work in progress joint with Guchuan Li and Elizabeth Tatum.