  We develop a comprehensive theory of twisted bilayer magnetism. Starting from
the first-principles calculations of two-dimensional honeycomb magnet CrI3, we
construct the generic spin models that represent a broad class of twisted
bilayer magnetic systems. Using Monte-Carlo method, we discover a variety of
non-collinear magnetic orders and topological magnons that have been overlooked
in the previous theoretical and experimental studies. As a function of the
twist angle, the collinear magnetic order undergoes the phase transitions to
the non-collinear order and the magnetic domain phase. In the magnetic domain
phase, we find that the spatially varying interlayer coupling produces the
magnetic skyrmions even in the absence of the Dzyaloshinskii-Moriya
interactions. In addition, we describe the critical phenomena of the magnetic
phase transitions by constructing the field theoretical model of the moire
magnet. Our continuum model well-explains the nature of the phase transitions
observed in the numerical simulations. Finally, we classify the topological
properties of the magnon excitations. The magnons in each phases are
characterized by the distinct mass gaps with different physical origins. In the
collinear ferromagnetic order, the higher-order topological magnonic insulator
phase occurs. It serves as a unique example of the higher-order topological
phase in magnonic system, since it does not require non-collinear order or
asymmetric form of the interactions. In the magnetic domain phases, the magnons
are localized along the domain wall and form one-dimensional topological edge
mode. As the closed domain walls deform to a open network, the confined edge
mode extends to form a network model of the topological magnons.
