DescriptionSuperinductors are inductors whose microwave characteristic impedances are greater than the resistance quantum, $R_{Q}=h/(2e)^{2}approx6.5kOmega$. They can be implemented using Josephson junction chains and high kinetic inductance nanowires. In this dissertation, we explore applications of superinductors in both implementations in superconducting quantum circuits. The dissertation consists of three parts. In the first part, we discuss the fluxon-parity-protected qubit consisting of a Cooper-pair box (CPB) shunted by a superinductor made of a chain of coupled asymmetric Superconducting Quantum Interference Devices (CASQUIDs). The spectroscopic measurement of a prototype of the fluxon-parity-protected qubit was performed. We observed almost complete suppression of the single fluxon tunneling across the CPB due to the destructive Aharonov-Casher interference when the offset charge on the CPB island was set to $e$ mod(2$e$). A fluxon-parity-protected qubit with a higher superinductance can potentially be used to perform fault-tolerant Clifford gates. In the second part, we studied the microwave losses in high-kinetic-inductance granular Aluminum films using superconducting coplanar-waveguide (CPW) resonators made of the films. We observed that the intrinsic losses in these resonators at low temperatures were limited by resonator coupling to the two-level systems (TLS) in the environment. The demonstrated internal quality factors are comparable with those for CPW resonators made of conventional superconductors. The characterized granular Aluminum films can be used to fabricate superinductors for a wide range of applications in quantum metrology and quantum information processing. In the third part, we discuss the one-dimensional Josephson metamaterial made of a similar structure as the superinductor used in the fluxon-parity-protected qubit. The metamaterial demonstrated strong Kerr nonlinearity with the Kerr constant tunable over a wide range from positive to negative values by the magnetic field. The metamaterial is promising for use as an active medium for quantum-limited Josephson traveling-wave parametric amplifiers.