We present the results from three gravitational-wave searches for coalescing compact binaries with component masses above 1M⊙ during the first and second observing runs of the Advanced gravitational-wave detector network. During the first observing run (O1), from September 12th, 2015 to January 19th, 2016, gravitational waves from three binary black hole mergers were detected. The second observing run (O2), which ran from November 30th, 2016 to August 25th, 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+3.1−0.7M⊙, and 85.1+15.6−10.9M⊙, and range in distance between 320+120−110 Mpc and 2750+1350−1320 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 Gpc−3y−1 for binary neutron stars and 9.7 - 101 Gpc−3y−1 for binary black holes, and determine a neutron star - black hole merger rate 90% upper limit of 610 Gpc−3y−1.