Integrated optical phased arrays, fabricated in advanced silicon-photonics platforms, enable manipulation and dynamic control of free-space light in a compact form factor, at low costs, and in a non-mechanical way. As such, integrated optical phased arrays have emerged as a promising technology for many wide-reaching applications, including LiDAR sensors and augmented-reality displays. In this thesis, novel integratedoptical-phased-array devices, systems, results, and applications are presented. First, beam-steering optical phased arrays for LiDAR are shown, including the first beam-steering optical phased arrays powered by monolithically-integrated onchip rare-earth-doped lasers, the first beam-steering optical phased arrays controlled using heterogeneously-integrated CMOS driving electronics, and the first single-chip coherent LiDAR with integrated optical phased arrays and CMOS receiver electronics. These demonstrations are important steps towards practical commercialization of lowcost and high-performance integrated LiDAR sensors for autonomous vehicles. Next, integrated optical phased arrays for optical manipulation in the near field are developed, including the first near-field-focusing integrated optical phased arrays, the first quasi-Bessel-beam-generating integrated optical phased arrays, and a novel active butterfly architecture for independent amplitude and phase control. These near-field modalities have the potential to advance a number of application areas, such as optical trapping for biological characterization, trapped-ion quantum computing, and laser-based 3D printing. Finally, a novel transparent integrated-phased-array-based holographic display is proposed as a highly-discreet and fully-holographic solution for the next generation of augmented-reality head-mounted displays; novel passive near-eye displays that generate holograms, the first integrated visible-light liquid-crystal-based phase and amplitude modulators, and the first actively-tunable visible-light integrated optical phased arrays are presented.