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The cataclysmic observations of event GW170817, first as gravitational wavesalong the inspiral motion of two neutron stars, then as a short $\gamma$-rayburst, and later as a kilonova, launched the era of multimessenger astronomy,and played a pivotal role in furthering our understanding on a number oflongstanding questions. Numerical modelling of such multimessenger sources isan important tool to understand the physics of compact objects and, moregenerally, the physics of matter under extreme conditions. In this review wepresent a unified view of various techniques used to obtain equilibrium andquasiequilibrium solutions for three astrophysically relevant relativistic,self-gravitating fluid systems: Binary neutron stars, black hole-disks, andmagnetized rotating neutron stars. These solutions are necessary not only formodeling such compact objects, but equally important, for providingself-consistent initial data in numerical relativity simulations. Instead ofpresenting the full details of the formulations and numerical algorithms, wefocus on painting the broadbrush picture of the methods developed to addressthese problems, and facilitate future work in the area.

Methods for relativistic self-gravitating fluids: From binary neutron stars to black hole-disks and magnetized rotating neutron stars