Almost any eukaryotic (non-bacterial) cell grows a cilium or flagellum - at some point in its life. These slender cell appendages serve multiple sensory and signaling functions, and, in addition, can be motile. Motile cilia and flagella play a key role in a number of fundamental life processes of cells and organisms: as examples, their regular bending waves propel sperm and pathogens, including trypanosomes (the pathogen of sleeping sickness). Inside our bodies, thousands of mechano-sensitive flagella on the surface of epithelial tissues sense blood flow or pump fluids, such as mucus in our airways and cerebrospinal fluid in our brain. During embryonic development, the chiral beat of cilia determine where left and right will be, by generating symmetry-breaking flows in a specific structure called the organizer. In all these examples, not only does the beat of cilia and flagella exert active forces on the surrounding fluid and sets it in motion but, conversely, external fluid flows exert hydrodynamic forces on beating cilia and flagella and change their beat. This wave form compliance renders the flagellum an active force sensor. Thus, cilia and flagella combine sensory and motility function in one. The interaction between complex fluid flows and actively beating cilia and flagella poses fundamental questions at the interface of physics and biology, with relevance for biological function: First, the mechano-responses of flagella play an important role for the mechano-navigation of flagellated swimmers, i.e. their ability to follow boundary surfaces as guidance cue or to actively swim up-stream in external currents, a process termed rheotaxis. In fact, this mechano-navigation has been attributed an important role in guiding sperm cells within the narrow oviduct on their sojourn to the egg, yet remains insufficiently understood. Next, collections of cilia on epithelial surfaces can show collective dynamics, such as phase-locking to a common frequency despite active noise, and meta-chronal waves (similar to a Mexican wave in a soccer stadium) that facilitate efficient fluid transport. Finally, mechano-sensing is found also in non-motile cilia, where elastic deflections of the cilium are detected by dedicated molecular force sensors (TRP-channels) to signal functional read-outs of fluid flow, e.g. during heart morphogenesis or kidney homeostasis. To date, we do not know in any quantitative terms how the flagellar beat responds to mechanical forces. This is partly due to the previous lack of high-precision imaging, but also the lack of a theoretical framework that can account for the many degrees of freedom of flagellar shape dynamics. Previously, we started to tackle this challenge and developed such a framework that integrates state-of-the-art data analysis of flagellar shape dynamics and realistic hydrodynamic simulations of the three-dimensional Stokes equation, to provide a concise description of the nonlinear dynamics of flagellar oscillations that singles out a small number of key degrees of freedom. Only such a reductionist approach makes it possible to run simulations fully parameterized by experiment. We propose an extension of this theoretical framework to concisely characterize active mechano-responses of beating cilia and flagella (using dimensionality reduction and limit cycle reconstruction to relate shape changes and hydrodynamic forces under different load scenarios). This will bring us into a prime position to address the nonlinear feedback loops between flagellar dynamics and external fluid flows, enabling us to generate mechanistic insight into how flagellar mechano-navigation works, as well as into the collective dynamics of many cilia and flagella. Thereby, using theory and established collaborations with experimental partners, we will generate fundamental insight into a ubiquitous model system for the role of mechanics for motility and development that was highly conserved during the course of evolution.