  A full subcategory of a Grothendieck category is called deconstructible if it
consists of all transfinite extensions of some set of objects. This concept
provides a handy framework for structure theory and construction of
approximations for subcategories of Grothendieck categories. It also allows to
construct model structures and t-structures on categories of complexes over a
Grothendieck category. In this paper we aim to establish fundamental results on
deconstructible classes and outline how to apply these in the areas mentioned
above. This is related to recent work of Gillespie, Enochs, Estrada, Guil
Asensio, Murfet, Neeman, Prest, Trlifaj and others.
