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In this dissertation, we estimate the population of different classes of BNSsystems that are visible to gravitational-wave observatories. Given that noultra-compact BNS systems have been discovered in pulsar radio surveys, weplace a 95\% confidence upper limit of $\sim$850 and $\sim$1100 ultra-compactneutron star--white dwarf and double neutron star (DNS) systems that arebeaming towards the Earth, respectively. We show that among all of the currentradio pulsar surveys, the ones at the Arecibo radio telescope have the bestchance of detecting an ultra-compact BNS system. We also show that adopting asurvey integration time of $t_{\rm int} \sim 1$~min will maximize thesignal-to-noise ratio, and thus, the probability of detecting an ultra-compactBNS system. Similarly, we use the sample of nine observed DNS systems to derivea Galactic DNS merger rate of $\mathcal{R}_{\rm MW} =37^{+24}_{-11}$~Myr$^{-1}$, where the errors represent 90\% confidenceintervals. Extrapolating this rate to the observable volume for LIGO, we derivea merger detection rate of $\mathcal{R} = 1.9^{+1.2}_{-0.6} \times \left(D_{\rmr}/100 \ \rm Mpc \right)^3 \rm yr^{-1}$, where $D_{\rm r}$ is the rangedistance for LIGO. This rate is consistent with that derived using the DNSmergers observed by LIGO. Finally, we measure the sense of rotation of theolder millisecond pulsar, pulsar A, in the DNS J0737--3039 system and find thatit rotates prograde with respect to its orbit. This is the first directmeasurement of the sense of rotation of a pulsar and a direct confirmation ofthe rotating lighthouse model for pulsars. This result confirms that the spinangular momentum vector is closely aligned with the orbital angular momentum,suggesting that kick of the supernova producing the second born pulsarJ0737--3039B was small.

Modeling the Galactic Compact Binary Neutron Star Population and Studying the Double Pulsar System