During the last few decades, the microelectronics industry has actively been investigating the potential for the functional integration of semiconductor-based devices beyond digital logic and memory, which includes RF and analog circuits, biochips, and sensors, on the same chip. In the case of gas sensor integration, it is necessary that future devices can be manufactured using a fabrication technology which is also compatible with the processes applied to digital logic transistors. This will likely involve adopting the mature complementary metal oxide semiconductor (CMOS) fabrication technique or a technique which is compatible with CMOS due to the inherent low costs, scalability, and potential for mass production that this technology provides. While chemiresistive semiconductor metal oxide (SMO) gas sensors have been the principal semiconductor-based gas sensor technology investigated in the past, resulting in their eventual commercialization, they need high-temperature operation to provide sufficient energies for the surface chemical reactions essential for the molecular detection of gases in the ambient. Therefore, the integration of a microheater in a MEMS structure is a requirement, which can be quite complex. This is, therefore, undesirable and room temperature, or at least near-room temperature, solutions are readily being investigated and sought after. Room-temperature SMO operation has been achieved using UV illumination, but this further complicates CMOS integration. Recent studies suggest that two-dimensional (2D) materials may offer a solution to this problem since they have a high likelihood for integration with sophisticated CMOS fabrication while also providing a high sensitivity towards a plethora of gases of interest, even at room temperature. This review discusses many types of promising 2D materials which show high potential for integration as channel materials for digital logic field effect transistors (FETs) as well as chemiresistive and FET-based sensing films, due to the presence of a sufficiently wide band gap. This excludes graphene from this review, while recent achievements in gas sensing with graphene oxide, reduced graphene oxide, transition metal dichalcogenides (TMDs), phosphorene, and MXenes are examined.