In this talk, I will discuss a new family of supersymmetric Wilson loop operators in N=4 SYM. These operators can be defined for any loop on a three-sphere in space-time and generically preserve two super-conformal charges. On the string side, via AdS/CFT duality, these loops map to surfaces which are 'pseudo-holomorphic' with respect to a novel almost-complex structure defined on a suitable subspace of AdS5xS5. Of particular interest is the subclass of loops lying on a two-sphere in space-time whose expectation value is conjectured to be computed exactly in terms of the analogous observables in bosonic 2d Yang-Mills on S2. Several evidences for this conjecture, both on the gauge theory and on the string theory side will be discussed.