The theory of quadrilateral lattices [1,2] provides unifying scheme for studying various distinguished integrable discrete equations, like the discrete Darboux system, the discrete BKP and CKP equations [3,4].Starting from the Geometric Integrablity Scheme some selected new results on the quadrilateral lattice, its basic reductions and transformations will be revieved with emphasizing the fundamental role of incidence geometry configura tions.Recent results on the noncommutative lattices [5] will be also discussed within this framework.