Seminaire du Laboratoire Jacques-Louis Lions, Sorbonne University, France, April 2021 (online) Your brain has its own waterscape: whether you are reading or sleeping, fluid flows around or through the brain tissue and clears waste in the process. These physiological processes are crucial for the well-being of the brain. In spite of their importance we understand them but little, and mathematical modelling could play a crucial role in gaining new insight. Surprisingly little attention has been paid to the mathematics and numerics of the brain’s waterscape however, and even fundamental knowledge is missing. After an introduction to brain physiology, I will discuss mathematical and numerical aspects relating to the brain's waterscape focusing on two scales - viewing the brain as a multi-network poroelastic medium at the macroscale, and zooming in to study electrical, chemical and mechanical interactions between brain cells at the microscale.