Gravitational theories differing from General Relativity may explain the accelerated expansion of the Universe without a cosmological constant. However, their viability crucially depends on a “screening mechanism” needed to suppress, on small scales, the fifth force driving the cosmological acceleration. I will discuss a scalar-tensor theory with first-order derivative self-interactions exhibiting such a mechanism, and present static screened solutions in this theory for both non-relativistic and relativistic stars. I will then describe how the screening mechanism behaves dynamically, showing results obtained with spherically symmetric simulations of non-linear stellar oscillations and gravitational collapse. Lastly, I will discuss how this type of screening behaves in binary neutron stars.