I will discuss a new class of 1/4-BPS surface operators of order type
in N=4 Yang-Mills theory and find their dual supergravity solutions.
The insertion of these operators can be described by a system of D3- and
D7-branes intersecting along a surface. Consistency requires that
the N=4 Yang-Mills theory be formulated in the D7-brane background
rather than in flat space. This extends the class of holographic field
theories dual to string theory beyond gauge theories in flat space.