This paper explores the intricate relationship between exact structures and triangulated categories, two fundamental concepts in modern homological algebra and category theory. Triangulated categories provide a robust framework for studying derived categories, stable module categories, and various constructions in algebraic geometry and topology, characterized by their distinguished triangles that encapsulate aspects of short exact sequences. However, the exactness properties traditionally associated with abelian categories are not directly present. We introduce and formally define what constitutes an "exact structure" on a triangulated category, examining different axiomatic approaches and their implications. The motivation stems from the desire to leverage the powerful tools of exact sequences and diagram chasing within the more general and often non-abelian context of triangulated categories. We delve into methods for constructing such structures, discussing their compatibility with the triangulated functorial properties, and explore the concept of exact functors between triangulated categories endowed with exact structures. Furthermore, the paper investigates applications where these exact structures offer new insights, particularly in linking triangulated categories to underlying abelian or exact categories. We present a detailed literature review of historical developments, a rigorous methodological framework for defining and analyzing exact structures, and a discussion of key results and open problems. The goal is to provide a comprehensive overview of this rich mathematical landscape and highlight its significance for future research in homological algebra and related fields.