Let F be a homogeneous polynomial defining a projective hypersurface X over a field K. The strength of F is equal to the minimum number r such that F = G_1 + ... + G_r, where G_i are reducible homogeneous polynomials. This invariant captures remarkable geometric properties of X. For example, when K is algebraically-closed, the strength of F bounds the codimension of the singular locus of X. This invariant is also studied in the context of number theory and additive combinatorics; we will discuss these contexts in addition to connections to recent developments in geometry.