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We present the results from three gravitational-wave searches for coalescingcompact binaries with component masses above 1$\mathrm{M}_\odot$ during thefirst and second observing runs of the Advanced gravitational-wave detectornetwork. During the first observing run (O1), from September $12^\mathrm{th}$,2015 to January $19^\mathrm{th}$, 2016, gravitational waves from three binaryblack hole mergers were detected. The second observing run (O2), which ran fromNovember $30^\mathrm{th}$, 2016 to August $25^\mathrm{th}$, 2017, saw the firstdetection of gravitational waves from a binary neutron star inspiral, inaddition to the observation of gravitational waves from a total of seven binaryblack 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 holeshave 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 - blackhole mergers were detected. In addition to highly significantgravitational-wave events, we also provide a list of marginal event candidateswith an estimated false alarm rate less than 1 per 30 days. From these resultsover the first two observing runs, which include approximately onegravitational-wave detection per 15 days of data searched, we infer mergerrates 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 fixedpopulation distributions, and determine a neutron star - black hole merger rate90% upper limit of $610$ $\mathrm{Gpc}^{-3}\,\mathrm{y}^{-1}$.

GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs