In this talk, I will present several results concerning a class of supersymmetric Wilson loop operators in N=4 SYM. These operators can be defined for any loop on a three-sphere and are in general 1/16-BPS. On the string theory side of the AdS/CFT duality, these supersymmetric Wilson loops are described by string worldsheets which are pseudo-holomorphic with respect to a novel almost complex structure defined on a AdS4xS2 subspace of AdS5xS5. A notable subclass of the general 1/16-BPS operators, which will be the main focus of this talk, is obtained by restricting the loop to lie on a S2 in space-time. In this case supersymmetry is doubled, and we propose a conjecture that the expectation value of these operators can be computed exactly in terms of the analogous observables in bosonic 2d Yang-Mills on S2, or equivalently by a gaussian matrix model. Several evidences for this conjecture, both on the gauge theory and on the string theory side, will be presented.