Physics-aware ML (PaML) aims to take the best from both physics-based modeling and state-of-the-art ML models to better solve scientific problems. A structured community of existing PaML methodologies that integrate prior physical knowledge or physics-based modeling into ML is built. We categorize PaML approaches into four groups based on the way physics and ML are combined, including physical data-guided ML (PDgML), physics-informed ML (PiML), physics-embedded ML (PeML), and physics-aware hybrid learning (PaHL).