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 $18.6_{-0.7}^{+3.2}mathrm{M}_odot$, and $84.4_{-11.1}^{+15.8} mathrm{M}_odot$, and range in distance between $320_{-110}^{+120}$ Mpc and $2840_{-1360}^{+1400}$ 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 assuming fixed population distributions, and determine a neutron star - black hole merger rate 90% upper limit of $610$ $mathrm{Gpc}^{-3},mathrm{y}^{-1}$.
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