This paper surveys recent work that is aimed at generalising the results and techniques of the Graph Minors Project of Robertson and Seymour to matroids.

Oxford University Press
G. Grimmett , C.J.H. McDiarmid (Colin)
Probability, Networks and Algorithms

Geelen, J, Gerards, A.M.H, & Whittle, G. (2007). Towards a matroid-minor structure theory. In G Grimmett & C.J.H McDiarmid (Eds.), Combinatorics, Complexity, and Chance. A tribute to Dominic Welsh. (pp. 72–82). Oxford University Press.