We present the results from three gravitational-wave searches for coalescing compact binaries with component masses above 1\(\mathrm{M}_\odot\) during the first and second observing runs of the Advanced gravitational-wave detector network. During the first observing run (O1), from September \(12^\mathrm{th}\), 2015 to January \(19^\mathrm{th}\), 2016, gravitational waves from three binary black hole mergers were detected. The second observing run (O2), which ran from November \(30^\mathrm{th}\), 2016 to August \(25^\mathrm{th}\), 2017, saw the first detection of gravitational waves from a binary neutron star inspiral, in addition to the observation of gravitational waves from a total of seven binary black hole mergers, four of which we report here for the first time: GW170729, GW170809, GW170818 and GW170823. For all significant gravitational-wave events, we provide estimates of the source properties. The detected binary black holes have total masses between \(18.6_{-0.7}^{+3.1}\mathrm{M}_\odot\), and \(85.1_{-10.9}^{+15.6} \mathrm{M}_\odot\), and range in distance between \(320_{-110}^{+120}\) Mpc and \(2750_{-1320}^{+1350}\) Mpc. No neutron star - black hole mergers were detected. In addition to highly significant gravitational-wave events, we also provide a list of marginal event candidates with an estimated false alarm rate less than 1 per 30 days. From these results over the first two observing runs, which include approximately one gravitational-wave detection per 15 days of data searched, we infer merger rates at the 90% confidence intervals of 110 - 3840 \(\mathrm{Gpc}^{-3}\,\mathrm{y}^{-1}\) for binary neutron stars and 9.7 - 101 \(\mathrm{Gpc}^{-3}\,\mathrm{y}^{-1}\) for binary black holes, and determine a neutron star - black hole merger rate 90% upper limit of 610 \(\mathrm{Gpc}^{-3}\,\mathrm{y}^{-1}\).