Astronomical transients provide a unique opportunity for probing the fundamental physics at work in compact objects by studying their behavior in both the spectral and temporal domains. Transient sources are often accompanied with collimated outflows, namely jets. These are seen in many different objects, such as active galactic nuclei (AGNs), gamma-ray bursts (GRBs), black hole X-ray binaries (XRBs) and tidal disruption events (TDEs). Despite decades of research, the answers to several fundamental questions remain unknown. These include: (I) Where and how are jets launched, accelerated and collimated? (II) What is the composition, magnetization, kinetic and radiative power of jets, and how are these related to the properties of the accretion disks? (III) What are the internal dynamics and physical conditions inside transient jets? Which sources fulfill the conditions that enable the acceleration of cosmic rays to ultra-high energies?The ultimate scientific goal of this proposal is to revolutionize our understanding of the transient sky by addressing these questions. For this task, I propose to build and implement several unique tools I have developed over the past years. I suggest three separate projects that address the above questions in different environments, in order to synergize the knowledge obtained. These include: (i) applying radiative tools with general relativistic magneto-hydrodynamic simulations to examine the predicted observed signal; (ii) Study novel dynamical and radiative process in structured jets; and (iii) construct a new model for particle acceleration in relativistic shock waves which considers particle feedback on the dynamics. The results of these theoretical studies will be directly compared to current and future data across the entire electromagnetic spectrum, allowing us to understand the fundamental physics at work in nature.