Perturbative QCD (pQCD) derived from first principles, is used to predict experimental observations involving large momentum transfer, such as high-energy jet productions in proton-proton collisions, and the strong interaction between the jet and the Quark-Gluon Plasma (QGP) medium created in nucleus-nucleus collisions. Recent experimental observations have shown that stronger energy-loss mechanism is at play for jets with large transverse momentum, which current perturbative approaches failed to describe. Utilizing an incoherent approach, I will derive an improved energy-loss mechanism that can provide accurate description of the nuclear modification at large jet momentum, which can restore the predictive power of pQCD and allow us to extract the transport property of the hot nuclear medium. The theory of pQCD also anticipates a saturation phenomenon, whereby the density of gluons tends to arrive at equilibrium between the splitting and recombination of gluon quantum fluctuations as the momentum fraction becomes smaller. Recent theoretical development have mitigated the negativity and instability problem that appears in next-to-leading order calculations of forward jet productions under the Color Glass Condensate framework that takes into account the gluon saturation phenomenon. I will also develop a numerical program which incorporates this new approach to implement saturation effects in order to provide a reliable tool in search of saturation signal in current proton-nucleus collisions. The electromagnetic (EM) properties of the nucleus is also of great interest in ultra-peripheral collision (UPC) physics, where the EM form-factor of the nucleus under the GTMD prescription provides a 5-dimensional Wigner distribution of the nucleus. I will also construct a framework using GTMD approach and recent UPC experimental data to analyse the different quantum effects that appears as the EM background in a nucleus-nucleus collision.