  In moir\'e crystals formed by stacking van der Waals (vdW) materials,
surprisingly diverse correlated electronic phases and optical properties can be
realized by a subtle change in the twist angle. Here, we discover that phonon
spectra are also renormalized in MoS$_2$ twisted bilayers, adding a new
perspective to moir\'e physics. Over a range of small twist angles, the phonon
spectra evolve rapidly due to ultra-strong coupling between different phonon
modes and atomic reconstructions of the moir\'e pattern. We develop a new
low-energy continuum model for phonons that overcomes the outstanding challenge
of calculating properties of large moir\'e supercells and successfully captures
essential experimental observations. Remarkably, simple optical spectroscopy
experiments can provide information on strain and lattice distortions in
moir\'e crystals with nanometer-size supercells. The newly developed theory
promotes a comprehensive and unified understanding of structural, optical, and
electronic properties of moir\'e superlattices.
