During the billions of years of the evolutionary journey, primitive polymers, involved in proto metabolic pathways with low catalytic activity, played critical roles in the emergence of modern enzymes with remarkable substrate specificity. The precise positioning of amino acid residues and the complex orchestrated interplay in the binding pockets of evolved enzymes promote covalent and non-covalent interactions to foster a diverse set of complex catalytic transformations. Recent efforts to emulate the structural and functional information of extant enzymes by minimal peptide based assemblies have attempted to provide a holistic approach that could help in discerning the prebiotic origins of catalytically active binding pockets of advanced proteins. In addition to the impressive sets of advanced biochemical transformations, catalytic promiscuity and cascade catalysis by such small molecule based dynamic systems can foreshadow the ancestral catalytic processes required for the onset of protometabolism. Looking beyond minimal systems that work close to equilibrium, catalytic systems and compartments under non-equilibrium conditions utilizing simple prebiotically relevant precursors have attempted to shed light on how bioenergetics played an essential role in chemical emergence of complex behaviour. Herein, we map out these recent works and progress where diverse sets of complex enzymatic transformations were demonstrated by utilizing minimal peptide based self-assembled systems. Further, we have attempted to cover the examples of peptide assemblies that could feature promiscuous activity and promote complex multistep cascade reaction networks. The review also covers a few recent examples of minimal transient catalytic assemblies under non-equilibrium conditions. This review attempts to provide a broad perspective for potentially programming functionality via rational selection of amino acid sequences leading towards minimal catalytic systems that resemble the traits of contemporary enzymes.