My talk explores the evolution of classical K-theory in the context of monoid algebras, stemming from the renowned Serre's Problem (SP). Serre's inquiry into whether projective modules over polynomial rings, with with coefficients coming from a field, are free or not, sparked the genesis of algebraic K-theory. I will trace the natural progression of K-theory in monoid algebras, highlighting solved problems and identifying promising avenues for future exploration. I'll also discuss some convex geometrical connections that make these entities more intriguing and enrich our understanding of these structures.