Gas kick early warning in deepwater drilling is challenged by weak precursors and multi-source noise, which can delay detection and increase false alarms under conventional single-signal thresholds. This narrative review synthesizes recent advances in gas kick early warning methods based on machine learning and organizes the evidence with a decision-oriented framework that links sensing observability, feature construction, model design, evaluation metrics, and well control actions. Three themes recur: multi-source fusion across surface, riser, and downhole channels; a shift from shallow statistical learners to deep and hybrid architectures; and increasing emphasis on estimating influx volume and rate within operational workflows. Engineering evidence indicates that a developing gas influx produces distributed, time-shifted signatures along the wellbore that may emerge first in downhole, riser, or surface measurements depending on circulation and operating conditions. These considerations motivate an integrated monitoring layout that combines topside mud logging streams, riser acoustics, and annular pressure while drilling (APWD) or other while-drilling measurements. This review clarifies how monitoring outputs can be integrated into managed pressure drilling workflows to close the loop from detection and tiered alerts to operational adjustments. An illustrative offshore test case is included solely to demonstrate reporting schema and deployment context; the reported trial demonstrated a reproducible lead time of at least 12 min relative to conventional mud-logging surveillance. Overall, the review provides comparative, evidence-based, and deployment-oriented guidance to support earlier and more reliable gas kick early warning in deepwater operations.