Motor Imagery-based (MI) Electroencephalography (EEG) has emerged as a leading solution in non-invasive Brain-Computer Interface (BCI) systems, leveraging its strong motor intention correlation to enable reliable neural decoding. However, practical implementation of MI confronts three persistent challenges: low signal-to-noise ratio, substantial variability across subjects or over time, and inherent signal nonstationarity. These fundamental limitations continue to hinder the widespread adoption and operational reliability of MI BCI systems. Despite advances in cross-variability decoding methods, there is a lack of systematic syntheses to guide technological evolution in MI BCI. To address these challenges, this review presents a comprehensive taxonomy of MI EEG cross-variability decoding studies from 2020 to 2025, systematically organizing advances in deep learning and transfer learning. We critically evaluate core algorithmic approaches, including Convolutional Neural Networks (CNN), transformers, feature alignment, domain adaptation, and meta-learning. We then explore the underlying mechanisms of these methods and assess their efficacy across key variability paradigms (mainly cross-subject and cross-session scenarios). Finally, we summarize key findings, highlight unresolved challenges, and outline promising future research directions. These advancements hold significant potential to bridge the gap between laboratory-based MI and real-world clinical and consumer applications.