Recent astrophysical observations suggest that, inside neutron stars, the speed of sound and the trace anomaly may not follow a simple extrapolation from normal-phase quark matter. This possible discrepancy has drawn attention because it could provide observational signatures of color superconductivity. On the theory side, QCD becomes weakly coupled at sufficiently high density, so perturbative methods can be applied. Weak-coupling frameworks that include the color-superconducting gap are well established and allow systematic, order-by-order improvements. In this talk, I summarize current observational constraints on the equation of state, compare them with state-of-the-art theoretical predictions, and discuss whether color superconductivity can occur in neutron-star cores.