Climate-related hazards alter livelihoods, mobility aspirations and household capacities across rural India, but the resulting population movements cannot be explained by climate exposure alone. This review examines how drought, rainfall variability, heat stress, agricultural uncertainty and resource insecurity intersect with rural–urban migration, and how Indian cities might accommodate mobile populations without transferring vulnerability from villages to hazardous urban settlements. It critically synthesizes peer-reviewed Indian empirical studies, major conceptual reviews and official reports, with particular attention to heterogeneous migration responses, livelihood adaptation, urban informality and policy coherence. Evidence from Indian household panels and city-level mixed-methods research associates drought and weather shocks with particular types of migration while demonstrating that irrigation, local non-farm income, migration costs, skills and social networks mediate mobility. Migrants may diversify household income through remittances, yet insecure labour, low-quality housing, heat exposure and limited service portability can generate new risks at destination. The review proposes a linked origin–corridor–destination framework integrating climate-resilient livelihoods, rights-based mobility and migrant-inclusive urban adaptation. It identifies priorities for subnational longitudinal evidence, causal evaluation of adaptation measures, smaller-city research, gender-sensitive analyses and interoperable social protection. Migration should be treated neither as inevitable climate displacement nor as a universally successful adaptation strategy, but as one possible outcome within a broader opportunity-and-constraint system.