The deep understanding of the physical properties of quantum materials requires the study crossing over from microscopic to macroscopic.New quantum phenomena emerge at the mesoscopic and macroscopic level,such as interference effects,quantum confinement effects,and charging effects.For structures with scales larger than 100 nanometers,the ab initio calculations are unfeasible.Tight-binding propagation methods(TBPMs)[1-5] are developed for the modeling of systems range from mesoscopic to macroscopic level,and applied for the calculations of electronic,transport and optical properties.We will give an introduction of the methods,and show their applications together with our recent progresses in the study of 2D materials,heterostructures and superstructures,such as the many-body enhancement of insulating states at the additional Dirac points in graphene-hBN heterostructures [6],the modification of optical gap in fluorographene due to(super)structure disorders [7],effects of disorder in the electronic and optical properties of semiconducting black phosphorus [8-9] and transition metal dichalcogenides [10],a new tight-binding model parametrization for black phosphorus with an arbitrary number of layers [11],quantum Hall effects in biased black phosphorus [12],and conductance fluctuations in 2D fractals [13].We will also show how to combine the TBPMs with other well-known numerical methods such as DFT-GW and molecular dynamics,and discuss briefly the extension to many-body problems.