This study presents a comprehensive PRISMA 2020-compliant systematic review of satellite remote sensing approaches used to monitor vegetation responses to climate change over the period 2000–2025. A total of 757 peer-reviewed studies were analysed to evaluate trends in sensor usage, spectral indices, machine learning (ML) and deep learning (DL) applications, geographic distribution, and methodological practices. Results indicate a rapid growth in research output, particularly after 2019, driven by the availability of high-resolution satellite data (e.g., Sentinel-2), cloud computing platforms, and advances in artificial intelligence. MODIS, Landsat, and Sentinel-2 emerged as dominant sensors, while NDVI remains the most widely used vegetation index despite known limitations. Random Forest and regression models continue to dominate analytical approaches, although DL methods such as CNNs and LSTMs are increasingly adopted. The review identifies significant geographic inequities, with over 80% of studies originating from Global North institutions, and highlights underrepresentation of critical ecosystems such as drylands, peatlands, and shrublands. Furthermore, inconsistent reporting of model performance metrics and limited adoption of open science practices constrain reproducibility and cross-study comparison. The study concludes by outlining key research gaps and providing strategic recommendations to advance the integration of multi-sensor data, improve methodological standardisation, and promote equitable and reproducible research in vegetation–climate remote sensing.