Non-equilibrium statistical mechanics is concerned with the problem of deriving the phenomenologically well-established macroscopic properties of matter in bulk from the underlying fundamental laws of nature governing the motion of the constituent particles. In spite of its long history and practical and theoretical importance, the foundations of this subject are vehemently debated to this day with a number of rival schools offering alternative and often mutually incompatible explanations. In this talk I will give an overview of a particular school of thought, known as the Brussels formalism. After a discussion of its cenceptual and physical content I will focus on attempts to provide a rigorous mathematical formulation of this formalism.