Hopf algebras (and variations of them) are the algebraic counterpart of (strict, rigid) tensor categories. As such, they appear as symmetries of different categorial, geometrical, and physical objects. In particular, several applications may be found in diverse areas of mathematics, physics, and theoretical computer sciences. Hopf algebras were already studied in the '60s and had a big impulse in the '80s after the work of Drinfeld on quantum groups. Despite of more than 60 years of study, not much is known about them. General results are sparse and the classification is only known for (quite) small dimensions or for families with different properties. This talk will be about a joint project with N. Andruskiewitsch and G. Carnovale in our attempt to determine finite-dimensional pointed Hopf algebras over finite-simple groups of Lie type. The main idea we exploit is the reduction of the problem to group-theoretical criteria to determine the finite-dimensionality of our objects, which boils down to the use of different properties of conjugacy classes, root systems and computational tools.