The quantum spectral curve (QSC) is currently the most concise formulation
of the spectral problem of planar N=4 SYM. I will describe the structure of
this Riemann-Hilbert problem and how it can be embedded in system of
Q-functions. A recent application is an efficient algorithm solving the QSC
perturbatively at weak coupling for operators belonging to the closed sl(2)
sector. I will outline this procedure and comment on the obtained results,
before finally discussing strategies to generalize the technique to any
operator.