Quantum systems are subject to dissipation as perfect isolation from the surrounding environment is impractical. Though this might wash out the intriguing quantum features that are absent in classical systems, proper engineering of dissipation, by contrast, opens up the possibility to not only prepare resilient quantum states but also attain dynamical properties unreachable in closed systems. The former provides a robust source for universal quantum computation and the latter transcends the conventional equilibrium physics bringing on genuinely new many-body phenomena.This work utilizes novel variational techniques to explore many-body effects in strongly correlated and/or interacting open quantum systems. After introducing these techniques in Part I, innovative solutions to several challenging problems in the context of non-equilibrium steady states are presented in Part II. In this part, we first address the issue of having genuine bistability in the steady state of open quantum systems. To this end, we develop a powerful framework to analyze stability in the long-time limit of a generic dissipative process with or without the detailed balance condition. The study of Toom's majority voting model in the presence of quantum fluctuations paves the way for engineering bistability using chiral jump operators. In a second step, we extend our variational method to approach otherwise intractable problems in the context of strongly interacting dissipative spin systems. Our method enables the estimation of steady-state properties across phase transitions. We exemplify this by simulating long-range interacting Rydberg gases undergoing different kinds of dissipation.In Part III, we turn our attention to dynamical properties of open quantum systems. We mainly focus on the classification of dynamical behaviors in quantum systems building upon the notion of elementary cellular automata (ECA). A master equation embedding of ECA dynamical rule 110 being capable of universal computation reveals the existence of a phase transition between chaotic and unpredictable behavior. We then complement the dynamical system with a second process in such a way that unpredictability coexists with quantum entanglement even in the long time limit. Finally, we demonstrate an efficient realization of many-body interactions required for such systems relying on a variational quantum simulation scheme that employs available qubit technologies.