Fluid-driven crack propagation concerns several areas of engineering, including structural, geotechnical, and petroleum engineering. The development of simulation tools for pressurized cracks propagating in realistic scenarios needs to tackle the complexity arising from the nonlinear hydro-mechanical coupling of the fluid and the cracked solid in a suitable framework for large-scale applications. In this lecture, I will introduce the governing equations of fluiddriven fracture propagation and discuss well-known propagation regimes where the problem can be treated analytically. I will then present a computational approach to model the hydro-mechanical coupling of the fracturing solid and the fluid flow inside the propagating cracks. Benchmarks in 2D and 3D demonstrate the capability of the computational framework to successfully deal with a priori unknown and arbitrarily intricate crack paths, and with the need for large-scale simulations. Time permitting, I will describe other recent efforts in developing advanced next-generation computational algorithms for large-scale simulation of complex material response, including mechanical instabilities and material failure.