Two-dimensional (2D) transition metal dichalcogenides (TMDs) have emerged as highly promising candidates for next-generation electronics owing to their atomically thin structures and surfaces devoid of dangling bonds. However, establishing high-quality metal contacts with TMDs presents a critical challenge, primarily attributed to their ultrathin bodies and delicate lattices. These distinctive characteristics render them susceptible to physical damage and chemical reactions when conventional metallization approaches involving "high-energy" processes are implemented. To tackle this challenge, the concept of van der Waals (vdW) contacts has recently been proposed as a "low-energy" alternative. Within the vdW geometry, metal contacts can be physically laminated or gently deposited onto the 2D channel of TMDs, ensuring the formation of atomically clean and electronically sharp contact interfaces while preserving the inherent properties of the 2D TMDs. Consequently, a considerable number of vdW contact devices have been extensively investigated, revealing unprecedented transport physics or exceptional device performance that was previously unachievable. This review presents recent advancements in vdW contacts for TMD transistors, discussing the merits, limitations, and prospects associated with each device geometry. By doing so, our purpose is to offer a comprehensive understanding of the current research landscape and provide insights into future directions within this rapidly evolving field.