The advent of time-domain astronomy has led to the discovery of a plethora of energetic transient phenomena showcasing a wide range of luminosities and durations, the latter spanning from a few seconds to a few months. While photons remain our primary observational tool, at high-energy they can interact with matter and radiation in their journey from the source to Earth, therefore carrying limited information about distant sources. Consequently, unraveling the mechanism powering transients solely through electromagnetic radiation can pose significant challenges, and the nature of most of these sources remains puzzling. Yet astrophysical transients also act as cosmic accelerators, producing cosmic rays and high-energy neutrinos, and they can emit gravitational waves. As each of these messengers carries unique information about their source, only by combining them can we gain a deep understanding of the most powerful phenomena occurring in the cosmos. Within the vibrant landscape of multi-messenger astronomy, the focus of this thesis is on high-energy neutrinos. Due to their feeble interaction with matter, neutrinos can travel large distances almost unhindered and therefore stand out as unique probes of the high-energy sky. This thesis endeavors to assess the potential of high-energy neutrinos to unravel the enigmatic nature of some transient phenomena.

The first part of this thesis offers a broad overview of multi-messenger astronomy and its current status, followed by a discussion on particle acceleration and radiative processes in high-energy astrophysics. Next, relevant transient sources and their connection with high-energy neutrinos are outlined. Finally, the thesis provides an overview of the currently operating and forthcoming electromagnetic as well as high-energy neutrino telescopes. These introductory Chapters pave the road towards discussing the potential of combining multi-wavelength and high-energy neutrino data.

The second and third parts of the thesis showcase original results from the published works concluded during the doctoral studies of the Ph.D. candidate. The first work presented in the second part makes use of state-of-the-art general relativistic magneto-hydrodynamic simulations of collapsar jets to show that high-energy neutrino production in regions deeply embedded in the outflow is favored only if the jet is magnetized. Importantly, this work proves that the subphotospheric high-energy neutrino signal is highly sensitive to the jet magnetization and can be used to reveal the presence of a choked jet in the source. The second work included in this part of the thesis investigates high-energy neutrino production at the optical jump, namely the sudden rebrightening observed in the optical lightcurve of some gamma-ray burst (GRB) afterglows. Notably, the findings of this work hint that high-energy neutrinos can enable us to test the medium surrounding the burst. The final work included in this part focuses on GRBs whose afterglow is observed at very-high-energy (VHE, & 100 GeV). By making use of multi-wavelength data and by requiring that the blastwave is transparent to W W pair production at the time of observation of VHE photons, this work hints that VHE GRBs may occur in low-density environments. These findings may have crucial implications for the progenitors of VHE GRBs.

High-energy neutrinos can also be combined with multi-wavelength data to probe the mechanisms powering emerging classes of high-energy transients, as outlined in the third part of the thesis. The first work presented in this part reveals that high-energy neutrinos can disentangle the mechanism powering Luminous Fast Blue Optical Transients (LFBOTs) while also constraining a region of the parameter space otherwise allowed by electromagnetic observations. Finally, we conclude this thesis with a work outlining the best strategy to carry out multi-messenger follow-up searches of transients stemming from collapsing massive stars. The key findings of this study prove that the neutrino signal is strongly correlated with the radio and X-ray bands if the transient is powered by interaction with a dense circumstellar medium and the spindown of a central magnetar, respectively. Importantly, this final work also proves that combining radio and X-ray data with the infrared-optical-ultraviolet lightcurve is pivotal to breaking the degeneracies in the transient parameter space.

As of today, high-energy neutrino astronomy is an extremely vibrant field. While the IceCube Neutrino Observatory successfully measured the diffuse flux of high-energy neutrinos, pinpointing their origin is extremely challenging due to the limited sensitivity of current instruments. Likewise, an increasing number of high-energy neutrinos is detected in association with astrophysical transients. Emerging neutrino telescopes such as IceCube-Gen2, KM3NeT, and GRAND anticipate a substantial enhancement in the detection capabilities of high-energy neutrinos, and they will finally give us the possibility to collect a large number of neutrino data. At the same time, the number of observed astrophysical transients is going to increase exponentially in the near future as high-cadence, wide-field surveys come online. With these encouraging developments on the horizon, we can expect to delve even deeper into the nature of the transient sources investigated in this thesis, unraveling further insights into their multi-messenger emission.