Agriculture is a major source of greenhouse gas (GHG) emissions but also offers significant potential for carbon sequestration. Carbon-neutral agriculture aims to balance emissions through mitigation practices and enhanced carbon storage. Advances in weather analytics, climate modeling, remote sensing, and artificial intelligence improve carbon accounting and climate-smart farm management. This review examines emission sources, carbon sequestration mechanisms, weather-based decision support, and Measurement, Reporting, and Verification (MRV) frameworks. Integrating weather analytics with carbon-neutral agricultural practices can improve sustainability, productivity, climate resilience, and contribute to achieving global net-zero emission targets.