Climate change has emerged as one of the most consequential and structurally complex threats to population health in the twenty-first century. Its impacts are not distributed equitably: populations in low- and middle-income countries (LMICs) bear a disproportionate share of climate-attributable health burdens despite contributing comparatively little to cumulative greenhouse gas emissions. This review provides an up-to-date, in-depth evaluation of the mechanisms by which the health of the developing world's population is at risk from climate change, and critically examines how the Sustainable Development Goals (SDGs), which include SDG 3 (Good Health and Well-being), SDG 2 (Zero Hunger), SDG 6 (Clean Water and Sanitation), and SDG 13 (Climate Action), may be at risk of irreversible impacts. The articles, multi-lateral agency reports and longitudinal epidemiological datasets published in the year 2019-2026, were analyzed and evidence synthesized in the following categories: climate sensitive diseases (including but not limited to vector-borne infections, waterborne diseases, respiratory illness, nutritional disorders and mental health outcomes). The review suggests climate change has several interconnected mechanisms of action, including biological, ecological, infrastructural, and socioeconomic, which increase the vulnerability of health of LMICs. However, it also enumerates six main intervention areas such as climate-resilient water and sanitation systems, integrated early warning networks, One Health surveillance, climate-smart agriculture, urban heat mitigation, and community health worker integration that can yield measurable co-benefits across a number of SDGs. Ensuring health equity in the face of increasing climate change requires a paradigm shift in global health governance, development finance and national adaptation planning, with the understanding that climate resilience and the achievement of SDG goals are intertwined and mutually reinforcing goals.