What is an "equation"? The best answer: a pair (p,q) of polynomials. A solution of this equation is an element r such that por = qor, where o denotes composition. So we are fully in the polynomial NEAR-ring rather than in polynomial rings. And from there, it is quite clear how to define equations in groups, modules, non-commutative rings, and the like. The criterion when an equation (or a system of equations) has a solution turns out to have a "near-ringish flavor" as well. Much of the presented material comes from joint work with Erhard Aichinger.