  Integrated electro-optic (EO) modulators are fundamental photonics components
with utility in domains ranging from digital communications to quantum
information processing. At telecommunication wavelengths, thin-film lithium
niobate modulators exhibit state-of-the-art performance in voltage-length
product ($V_\pi$L), optical loss, and EO bandwidth. However, applications in
optical imaging, optogenetics, and quantum science generally require devices
operating in the visible-to-near-infrared (VNIR) wavelength range. In this
work, we realize VNIR amplitude and phase modulators featuring $V_\pi$L's of
sub-1 V$\cdot\,$cm, low optical loss, and high bandwidth EO response. Our
Mach-Zehnder modulators exhibit a $V_\pi$L as low as 0.55 V$\cdot\,$cm at 738
nm, and EO bandwidths in excess of 35 GHz. Furthermore, we highlight the new
opportunities these high-performance modulators offer by demonstrating the
first integrated EO frequency combs at VNIR wavelengths, with over 50 lines and
tunable spacing, and the first frequency shifting of pulsed light beyond its
intrinsic bandwidth (up to 7x Fourier limit) by an EO shearing method.
