  We investigate the moir\'e band structures and the strong correlation effects
in twisted bilayer MoTe$_2$ for a wide range of twist angles, employing a
combination of various techniques. Using large-scale first principles
calculations, we pinpoint realistic continuum modeling parameters, subsequently
deriving the maximally localized Wannier functions for the top three moir\'e
bands. Simplifying our model with reasonable assumptions, we obtain a minimal
two-band model, encompassing Coulomb repulsion, correlated hopping, and spin
exchange. Our minimal interaction models pave the way for further exploration
of the rich many-body physics in twisted MoTe$_2$. Furthermore, we explore the
phase diagrams of the system through Hartree-Fock approximation and exact
diagonalization. Our two-band exact diagonalization analysis underscores
significant band-mixing effects in this system, which enlarge the optimal twist
angle for fractional quantum anomalous Hall states.
