The paper discusses results in main problems of vector optimization. Optimality notions and general existence theorems presented with an emphasis on proper efficiency. Norm scalarization in normed spaces ordered by general convex cone and other scalar representations are considered. For duality, we propose a scheme of constructing dual problems in an axiomatic approach, which includes Lagrangean duality as a special case. Furthermore, both necessary optimality conditions and sufficient conditions are obtained under relaxed assumptions and for general problems so that the Pontryagin maximum principle for cooperative differential gemes can be derived as consequences. Finally, we extend Ekeland's variational principle to vector optimization problems in a general setting.