Metal oxide semiconductor (MOS) gas sensors are an important part of electronic nose technology because they are sensitive, cheap, and work well with microfabrication for system integration. But sensor drift makes them less useful for long-term, continuous gas monitoring. Changes in how sensors respond over time make pattern recognition models that were trained at first less accurate. This review looks at new ways to deal with sensor drift, with a focus on transfer learning and deep learning methods that have been developing continuously in the last five years. It emphasizes the shift from conventional recalibration and component correction to sophisticated methodologies, including deep domain adaptation, contrastive representation learning, and attention-based models. The review does not just list these methods; it also analyzes their pros and downsides, especially in situations where there is not much labeled data, drift is hard to anticipate, or the computational resources are limited, which is often the case with edge sensors.