Quantifying forest carbon is crucial for informing decisions and policies that will protect the planet. Machine learning (ML) and remote sensing (RS) techniques have been used to do this task more effectively, yet there lacks a systematic review on the most recent ML methods and RS combinations, especially with the consideration of forest characteristics. This study systematically analyzed 25 papers meeting strict inclusion criteria from over 80 related studies, identifying 28 ML methods and key combinations of RS data. Random Forest had the most frequent appearance (88\% of studies), while Extreme Gradient Boosting showed superior performance in 75\% of the studies in which it was compared with other methods. Sentinel-1 emerged as the most utilized remote sensing source, with multi-sensor approaches (e.g., Sentinel-1, Sentinel-2, and LiDAR) proving especially effective. Our findings provide grounds for recommending best practices in integrating machine learning and remote sensing for accurate and scalable forest carbon stock estimation.