The in-spiral of compact binary systems consisting of a neutron star paired with either a black-hole or another neutron star produces distortions in space-time known as gravitational waves (GW). In the presence of sufficient ejecta, electromagnetic phenomena such as short-duration gamma-ray bursts (SGRBs) or kilonovae can be produced. In this thesis, I explore the environments, redshifts, and host galaxy demographics of these compact binaries. Using my Redshift Electromagnetic Localisation and Deduction Algorithm (zELDA), I seed BPASS and COSMIC evolved binaries into hydro-dynamical galaxies from the EAGLE simulation. I then trace the orbits of the binaries until they merge. I apply a selection criterion to a simulated SGRB sample to gauge the consistency with observations. I find agreements with the observed redshifts, host galaxy demographics, and offsets. I predict 16 -40% of SGRB events would appear "host-less", i.e. sources that merge with high impact parameters or have faint hosts (H > 26). Given the close proximity of GW170817 at ~ 40Mpc, I consider the constraints on a local population of low-luminosity SGRBs. I gauge the likelihood of SGRBs with host galaxies within < 200Mpc. I get an all-sky rate of < 6 yr⁻¹ using well-localised bursts (with precisions of ~ arcmin - arcsec) from 'Swift'/BAT, corresponding to ~ 8% of 'Swift' SGRBs. By cross-correlating poorly localised bursts from the CGRO/BATSE and Fermi/GBM with galaxies within < 100Mpc, I find a weaker constraint of £ 12 yr⁻¹ for the all-sky rate. I conduct a separate search to constrain the rate of nearby (d < 11Mpc) giant flares from Soft Gamma-Ray Repeaters (SGRs) and place an upper limit of < 3 yr⁻¹. I conclude this thesis by commenting on the implications of our findings on future studies.
