The thesis studies non-equilibrium stochastic particle systems, especially in the context of self-organised criticality. With increasing degree of complexity, different theoretical methods are explored, drawing upon the probability theory of branching processes and statistical field theory. The concept of "criticality" and its typical signatures are carefully examined in non-equilibrium
complex systems and exactly calculated for branching particle systems to identify universal features beyond the universality class. New theoretical results on the critical density of Abelian Manna model are found. Field theoretical approach is discussed to highlight the importance of dynamical correlations in certain models, and is generalised to accommodate critical
reaction-diffusion processes on graphs.