The first detection of gravitational waves from a neutron star-neutron star merger, GW170817, has opened up a new avenue for constraining the ultradense-matter equation of state (EOS). The deviation of the observed waveform from a point-particle waveform is a sensitive probe of the EOS controlling the merging neutron stars structure. In this topical review, I discuss the various constraints that have been made on the EOS in the year following the discovery of GW170817. In particular, I review the surprising relationship that has emerged between the effective tidal deformability of the binary system and the neutron star radius. I also report new results that make use of this relationship, finding that the radius inferred from GW170817 lies between 9.8 and 13.2 km at 90% confidence, with distinct likelihood peaks at 10.8 and 12.3 km. I compare these radii, as well as those inferred in the literature, to X-ray measurements of the neutron star radius. I also summarize the various maximum mass constraints, which point towards a maximum mass < 2.3 M_sun, depending on the fate of the remnant, and which can be used to additionally constrain the high-density EOS. I review the constraints on the EOS that have been performed directly, through Bayesian inference schemes. Finally, I comment on the importance of disentangling thermal effects in future EOS constraints from neutron star mergers.
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