This paper gives an informal introduction to structure theory for minor- closed classes of matroids representable over a fixed finite field. The early sections describe some historical results that give evidence that well-defined structure exists for members of such classes. In later sections we describe the fundamental classes and other features that necessarily appear in structure theory for minor-closed classes of matroids. We conclude with an informal statement of the structure theorem itself. This theorem generalises the Graph Minors Structure Theorem of Robertson and Seymour.
Cambridge University Press
London Mathematical Society Lecture Note Series
Networks and Optimization

Geelen, J., Gerards, B., & Whittle, G. (2013). Structure in minor-closed-classes of matroids. In Surveys in Combinatorics (pp. 327–362). Cambridge University Press. doi:10.1017/CBO9781139506748.009