We study the theory of matroid Steiner families introduced recently by \textit{C. J. Colbourn} and \textit{W. R. Pulleyblank} in this journal [Ser. B 47, No. 1, 20-31 (1989)], as a generalization of Steiner trees to matroids. We show that these families are equivalent to matroid ports. Using this equivalence we develop a new class of Steiner families which arise out of affine systems. The latter half of the paper deals with the combinatorial structure of the associated Steiner complexes. We develop an enumerative theory for these complexes that generalizes a well-known theory about matroid complexes.