  This review work addresses the recent advances in solving more comprehensive
Hamiltonians. The generalized tight-binding model is developed to investigate
the feature-rich quantization phenomena in emergent 2D materials. The
mutli-orbital bondings, the spin-orbital interactions, the various geometric
structures, and the external fields are taken into consideration
simultaneously. Specifically, the IV-group layered systems, black phosphorus
and MoS$_{2}$ exhibit the unique magnetic quantization. This is clearly
indicated in three kinds of Landau levels (LLs), the orbital-, spin- and
valley-dependent LL groups, the abnormal LL energy spectra, and the splitting,
crossing and anticrossing behaviors. A detailed comparison with the
effective-mass model is made. Some theoretical predictions have been confirmed
by the experimental measurements.
