In this paper, the electrically-tunable liquid crystal (LC) lenses and the applications are reviewed. We introduce the basic mechanism of LC phase modulation first. LC lenses are categorized based on different operating principles: 1) Gradient Index (GRIN) LC lenses with a homogeneous cell gap, 2) non-GRIN LC lenses with an inhomogeneous cell gap, 3) diffractive LC lenses, and 4) LC lenses controlled by polarizations. To remove the polarization independency, we also summarize polarization independent LC phase modulations. Many promising applications based on LC lenses are also summarized, such as imaging system, pico projectors, optical zoom systems, ophthalmic applications, and solar systems.