In this talk, I will present recent results on the limiting theorems of billiards with cusps, focusing on two key types: finite cusp and infinite cusp billiards. For finite cusp billiards, which are ergodic and mixing systems, I will discuss the rates of mixing and the convergence to stable laws. Moving to infinite cusp billiards,  the billiard map preserves an infinite measure, and we prove nonstandard limit theorems such as the Law of Large Numbers (LLN) and Functional Central Limit Theorems (FCLT) in this infinite measure context. Additionally, I will outline results for the billiard flow, which preserves either finite or infinite volume, leading to classical FCLT when the volume is finite. These findings contribute to a deeper understanding of the long-term statistical properties of both finite and infinite measure billiards.