GW170817 is the very first observation of gravitational waves originating fromthe coalescence of two compact objects in the mass range of neutron stars, accompaniedby electromagnetic counterparts, and offers an opportunity to directly probe the internalstructure of neutron stars. We perform Bayesian model selection on a wide range of theoreticalpredictions for the neutron star equation of state. For the binary neutron star hypothesis, wefind that we cannot rule out the majority of theoretical models considered. In addition, thegravitational-wave data alone does not rule out the possibility that one or both objects werelow-mass black holes. We discuss the possible outcomes in the case of a binary neutron starmerger, finding that all scenarios from prompt collapse to long-lived or even stable remnantsare possible. For long-lived remnants, we place an upper limit of1.9kHz on the rotation rate.If a black hole was formed any time after merger and the coalescing stars were slowly rotating,then the maximum baryonic mass of non-rotating neutron stars is at most3.05M, and threeequations of state considered here can be ruled out. We obtain a tighter limit of2.67Mforthe case that the merger results in a hypermassive neutron star.