The theoretical description of stars is plagued with severe scale problems: the many physical processes at play act on vastly different spatial and temporal scales. The classical approach to deal with this problem has been to formulate the underlying equations assuming spherical symmetry and hydrostatic equilibrium thus allowing for (numerical) solutions that explain the main phases of stellar evolution and reproduce many observables. This success, however, came at a price: casting inherently multidimensional physical processes in a one-dimensional framework required strong parametrization and sometimes even tinkering with the underlying physics. This diminishes the predictive power of stellar models and improvements are required to interpret and guide current and future observations. The next generation of stellar models clearly has to be build on multidimensional simulations. Are current (super-)computational resources sufficient to meet this challenge? What numerical techniques are required to enable simulations of challenging multi-physics, multi-scale stellar models? I will discuss three examples where a one-dimensional treatment clearly fails: convection and hydrodynamical instabilities ins stellar interiors, stellar explosions, and binary stellar evolution. These cases illustrate how the rapid evolution of computational astrophysics enables progress in stellar modeling.