Surface operators in supersymmetric gauge theories and their operator product expansion

Surface operators are nonlocal operators supported on two dimensional submanifolds naturally inhabited in 4d field theories. They play an important role in ramified geometric Langlands program, understanding different phases of strong dynamics, and in studying some coupled 4d-2d systems. I shall begin talking about three descriptions of surface operators, each carries a different flavor yet the matching among them can be very informative. Then we proceed to some computable cases (a la, operator product expansion of BPS surface operators) in N=2 and N=4 theories and finally to possible applications.