  Accurate hydrological understanding and water cycle prediction are crucial
for addressing scientific and societal challenges associated with the
management of water resources, particularly under the dynamic influence of
anthropogenic climate change. Existing reviews predominantly concentrate on the
development of machine learning (ML) in this field, yet there is a clear
distinction between hydrology and ML as separate paradigms. Here, we introduce
physics-aware ML as a transformative approach to overcome the perceived barrier
and revolutionize both fields. Specifically, we present a comprehensive review
of the physics-aware ML methods, building a structured community (PaML) of
existing methodologies that integrate prior physical knowledge or physics-based
modeling into ML. We systematically analyze these PaML methodologies with
respect to four aspects: physical data-guided ML, physics-informed ML,
physics-embedded ML, and physics-aware hybrid learning. PaML facilitates
ML-aided hypotheses, accelerating insights from big data and fostering
scientific discoveries. We first conduct a systematic review of hydrology in
PaML, including rainfall-runoff hydrological processes and hydrodynamic
processes, and highlight the most promising and challenging directions for
different objectives and PaML methods. Finally, a new PaML-based hydrology
platform, termed HydroPML, is released as a foundation for hydrological
applications. HydroPML enhances the explainability and causality of ML and lays
the groundwork for the digital water cycle's realization. The HydroPML platform
is publicly available at https://hydropml.github.io/.
