This project explores strong-gravity phenomena involving black holes in the context of high-energy physics applications and astrophysical observations including gravitational waves. The proposed studies can be loosely classified into four groups with considerable overlap. (i) Fundamental fields in strong gravity. Fundamental fields coupled to curvature are essential for cosmological models, for explaining the nature of dark matter or to extend the Standard Model of particle physics. In addition, scalar fields are often used as proxy for other, more complex interactions. Through numerical, perturbative and analytical modeling, we will explore the dynamics and wave emission of neutron stars and black holes in dark-matter environments and infer bounds on axion-like particles. (ii) Stability of black holes. The physical stability of black-hole solutions with or without the presence of fundamental matter fields will be studied. Such solutions represent possible end states of the dynamical processes and their importance critically relies on whether they form long-term stable spacetimes. (iii) Modified theories of gravity. Modifications and extensions of general relativity are being explored for a variety of reasons ranging from cosmological observations to attempts to unify general relativity with quantum mechanics. We will explore observable effects of various such theories in astrophysical systems with a particular focus on gravitational-wave and electromagnetic signatures, that could allow us to test general relativity against modified theories of gravity. (iv) High-energy collisions. The gravitational interaction of ultrarelativistic collisions will be modeled numerically and perturbatively to probe the possibility of black-hole formation in the framework of TeV gravity scenarios.