  A d\'evissage-type theorem in algebraic $K$-theory is a statement that
identifies the $K$-theory of a Waldhausen category $\mathscr{C}$ in terms of
the $K$-theories of a collection of Waldhausen subcategories of $\mathscr{C}$
when a d\'evissage condition about the existence of appropriate finite
filtrations is satisfied. We distinguish between d\'evissage theorems of single
type and of multiple type, depending on the number of Waldhausen subcategories
and their properties. The main representative examples of such theorems are
Quillen's original d\'evissage theorem for abelian categories (single type) and
Waldhausen's theorem on spherical objects for more general Waldhausen
categories (multiple type). In this paper, we study some general aspects of
d\'evissage-type theorems and prove a general d\'evissage theorem of single
type and a general d\'evissage theorem of multiple type.
