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.

Matroids, geometric lattices (msc 05B35)
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.