  Motivated by recent observation of nematicity in Moir\'{e} systems, we study
three different orbital orders that potentially can happen in Moir\'{e}
systems: (1) the nematic order; (2) the valley polarization; and (3) the
"compass order". Each order parameter spontaneously breaks part of the spatial
symmetries of the system. We explore physics caused by the quantum fluctuations
close to the order-disorder transition of these order parameters. Especially,
we recognize that the symmetry of the Moir\'{e} systems leads to a crucial
difference of the effective theory describing the nematic order from the
standard Hertz-Millis formalism. We demonstrate that this key difference may
lead to a special non-Fermi liquid behavior near the order-disorder nematic
transition, different from the standard non-Fermi liquid behavior usually
expected when a Fermi surface is coupled to the critical fluctuations of
orbital orders. We also discuss the interplay of the three order parameters and
the possible rich phase diagram at finite temperature. Within the three orbital
orders, the valley polarization and the "compass order" likely strongly compete
with the superconductor.
