"In several classical examples discrete surfaces naturally arise as pairs consisting of combinatorially dual nets describing the ""same"" surface. These examples include Koebe polyhedra, discrete minimal surfaces, discrete CMC surfaces, discrete confocal quadrics, and pairs of circular and conical nets. Motivated by this observation we introduce a discretization of parametrized surfaces via binets, which are maps from the vertices and faces of the square lattice into space. We look at discretizations of various types of parametrizations using binets. This includes conjugate binets, orthogonal binets, Gauß-orthogonal binets, principal binets, Kœnigs binets, and isothermic binets. Those discretizations are subject to the transformation group principle, which means that the different types of binets satisfy the corresponding projective, Möbius, Laguerre, or Lie invariance respectively, in analogy to the smooth theory. We discuss how the different types of binets generalize well established notions of classical discretizations. This is based on joint work with Niklas Affolter and Felix Dellinger."