Two-dimensional heterostructures (2D HSs) have emerged as a new class of materials where dissimilar 2D materials are combined to synergise their advantages and alleviate shortcomings. Such a combination of dissimilar components into 2D HSs offers fascinating properties and intriguing functionalities attributed to the newly formed heterointerface of constituent components. Understanding the nature of the surface and the complex heterointerface of HSs at the atomic level is crucial for realising the desired properties, designing innovative 2D HSs, and ultimately unlocking their full potential for practical applications. Therefore, this review provides the recent progress in the field of 2D HSs with a focus on the discussion of the fundamentals and the chemistry of heterointerfaces based on van der Waals (vdW) and covalent interactions. It also explains the challenges associated with the scalable synthesis and introduces possible methodologies to produce large quantities with good control over the heterointerface. Subsequently, it highlights the specialised characterisation techniques to reveal the heterointerface formation, chemistry and nature. Afterwards, we give an overview of the role of 2D HSs in various emerging applications, particularly in high-power batteries, bifunctional catalysts, electronics, and sensors. In the end, we present conclusions with the possible solutions to the associated challenges with the heterointerfaces and potential opportunities that can be adopted for innovative applications.