You could fly every day of your life in a commercial aircraft for twenty thousand years without suffering a fatal accident. This extraordinary level of safety is the product of decades of engineering and materials science research. Simultaneously, engineers have strived to produce lighter and stronger aircraft, with increased range and metals have thus been gradually replaced by lighter advanced composite materials, which take up more than half of the structural weight of today's most advanced aircraft. Such progress has been largely enabled by modeling and simulation of materials and structures, which have revolutionized design by enabling engineers to investigate virtually various design strategies. This presentation will focus on the challenges which have been posed, are posed, and will be posed to such modeling and simulation tools in the strive to predict the durability of lighter, stronger, longer-ranging and more reliable aircraft. We will also discuss several applications where interfaces are key to the behavior of mechanical systems, ranging from composite aircraft structures to surgical simulators, and we will present and compare different alternatives to discretize problems involving moving and free interfaces. Finally, we will define digital twins and investigate their potential in engineering and biomedical applications.