Both binary neutron star (BNS) and neutron star–black hole (NSBH) mergers radiate gravitational waves (GWs) as they gradually spiral inwards. Once they merge, they emit electromagnetic (EM) radiation that is potentially detectable across the entire EM spectrum, from hours to years after the coalescence. Right after the merger, a short burst of gamma-rays is followed by an hours to days long optical/near infrared (NIR) transient (i.e. kilonova (KN)), which is powered by the decay of the r-process nucleosynthesis elements. Depending on the angle of the gamma-ray burst (GRB) relative to Earth, a seconds to years long afterglow can be detected from radio to X-rays. The EM radiation from these mergers has shed light into different fields of physics and astronomy: they are sources of GWs, a site of rapid neutron-capture process (r-process) nucleosynthesis, and promising standard candles. However only one BNS merger has been studied in detail: AT2017gfo, the EM counterpart to GRB 170817A/GW170817. This thesis focuses on the opticalsearches of these multi-messenger sources using wide field of view (FOV) telescopes. The first chapter of this thesis describes the systematic search for optical counterparts to short gamma-ray bursts (SGRBs). We used the Zwicky Transient Facility (ZTF) to follow-up 10 short duration GRBs detected by the Fermi Gamma- ray Burst Monitor (GBM). We covered areas between 250 and 3000 deg2, and followed-up more than 60 objects, photometrically and spectroscopically. While we did not find a counterpart to a compact binary merger, we used the ZTF magnitude limits (i.e. ∼ 21 mag in the r-band) to compare to SGRB afterglows and KN models, to show that our searches are sensitive to most KN models up to 200 Mpc. However, the majority of SGRB afterglows in the literature have been found at relatively higher redshifts (i.e. mean z ∼ 0.5), making them fainter than our magnitude limits. Moreover, we explore the efficiency of our searches and we determine our searches have probed between redshift 0.16-0.4, depending on the energy models assumed for the SGRBs. Future campaigns can expand the horizon to redshift 0.2-0.7. The second part of this thesis is about the discovery of the shortest gamma-ray burst coming from a collapsing massive star. In the context of the optical follow-up of short GRBs with ZTF, we triggered target-of-opportunity (ToO) observations in the error region of GRB 200826A, a 1.13 sec duration GRB. There we found the afterglow of the burst, ZTF20abwysqy, with an optical decay rate ∼ 1 mag/day. The afterglow was additionally X-ray and radio bright. At the redshift of the host galaxy z = 0.74 , its hardness - intensity relation (i.e. Epeak,z − Eγ,iso) is consistent with the long GRB population, puzzling the community. We present the afterglow and host galaxy analysis, along with Gemini Multi-Object Spectrograph (GMOS) observations that show a rising source in the i-band that could only be explained by an underlying supernova. The third chapter of the thesis describes the optical follow-up of gravitational wave events using the ZTF. We describe the observing strategy, as well as the selection and monitoring of GW counterpart candidates. Our ToO strategy allowed us to sift through ∼ 2 million sources to select ∼ 160 candidates for follow-up. We apply this strategy to search for 13 GW alerts during the third LIGO/Virgo observing run (O3). Particularly, we describe the case of the first BNS merger in O3, S190425z, and two NSBH mergers, S200105ae and S200115j. As no counterpart was found for any of the GW events, we use the photometric limits of our searches to compare to KN models. Finally, we explore how the upcoming Rubin Observatory will be able to serendipitously find KNe, independently from GW or SGRB triggers. For this, we simulated the universe accessible to the survey and use it to derive contamination rates for different classes of transients. When using a filtering scheme based on the magnitude evolution of the sources, we find that ∼90% of the sources that fade faster than 0.4 mag/day are either GRB afterglows or supernova (SN) IIb shock breakout. This strategy is only capable of retrieving ∼3% of the generated KNe, mainly due to the fast fading nature of the KNe and their intrinsic low luminosity. We propose that future filtering schemes should take into consideration not just the detections, but the difference in magnitudes, ∆m, between the last detection and the subsequent limiting magnitude. Additional information as color, host galaxy or NIR counterparts on future NIR surveys could also improve the selection.