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A first order structure is homogeneous if any partial automorphism defined on a finite set extends to an automorphism of the full structure. I will present the first steps towards a classification of homogeneous structures which have few finite substructures. Peter Cameron and Dugald Macpherson conjectured some 30 years ago that such structures are tree-like or order-like. Model-theoretic results on NIP theories can be used to classify the order-like case. Applications include the classification of homogeneous structures in a language consisting of n linear orders and their reducts.