Systems of polynomial equations arise from many problems in applied mathematics. Solving such systems is considered a challenging computational problem. An important class of numerical solving methods converts the problem into a system of coupled eigenvalue problems. In order to perform this conversion one has to choose a representation for an algebra naturally associated to the equations. Standard choices (coming from Gröbner bases, border bases, resultants ...) may show some very bad, numerical behaviour, even for generic systems. Truncated normal form methods generalise all the aforementioned approaches and are designed to avoid these numerical issues. I will introduce the theory and give many examples. This is joint work with Bernard Mourrain and Marc Van Barel.