Motivated by recent experimental measurements on pressure-driven phase transitions in Mott insulators as well as the new iron pnictide superconductors, we show that first principles Car-Parrinello molecular dynamics calculations are a powerful method to describe the microscopic origin of such transitions. We present results for (i) the pressure-induced insulator to metal phase transition in the prototypical Mott insulator TiOCl as well as (ii) the pressure-induced structural and magnetic phase transitions in the family of correlated metals AFe(2)As(2) (A = Ca, Sr, Ba). Comparison of our predictions with existing experimental results yields very good agreement.