Integrated photonics is a powerful platform that can improve the performance and stability of optical systems while providing low-cost, small-footprint, and scalable alternatives to implementations based on free-space optics. While great progress has been made on the development of low-loss integrated photonics platforms at telecom wavelengths, the visible wavelength range has received less attention. Yet, many applications utilize visible or near-visible light, including those in optical imaging, optogenetics, and quantum science and technology. Here we demonstrate an ultra-low-loss integrated visible photonics platform based on thin-film lithium niobate on an insulator. Our waveguides feature ultra-low propagation loss of 6 dB/m, while our microring resonators have an intrinsic quality factor of 11 million, both measured at 637 nm wavelength. Additionally, we demonstrate an on-chip visible intensity modulator with an electro-optic bandwidth of 10 GHz, limited by the detector used. The ultra-low-loss devices demonstrated in this work, together with the strong second-and third-order nonlinearities in lithium niobate, open up new opportunities for creating novel passive and active devices for frequency metrology and quantum information processing in the visible spectrum range.