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2-D transition metal dichalcogenides (TMDs) are promising materials for CMOS application due to their ultrathin channel with excellent electrostatic control. TMDs are especially well suited for tunneling field-effect transistors (TFETs) due to their low-dielectric constant and their promise of atomically sharp and self-passivated interfaces. Here, we experimentally demonstrate band-to-band tunneling (BTBT) in Van der Waals heterostructures formed by MoS₂ and MoTe₂. Density functional theory simulations of the band structure show our MoS₂-MoTe₂ heterojunctions have a staggered band alignment, which boosts BTBT compared to a homojunction configuration. Low-temperature measurements and electrostatic simulations provide understanding toward the role of Schottky contacts and the material thickness on device performance. Negative differential transconductance-based devices were also demonstrated using a different device architecture. This paper provides the prerequisites and challenges required to overcome at the contact region to achieve a steep subthreshold slope and high ON-currents with 2-D-based TFETs.