Thus far, we have examined quantum computing based on electron states in atoms, ions and semiconductor structures. In this chapter, we will examine quantum states in superconductors and their application as qubits. This chapter is particularly extensive due to the large variety of possible superconducting quantum circuits. We introduce superconductivity and examine the three main types of superconducting qubit: the flux qubit, the charge qubit and the phase qubit. We will also examine the transmon qubit and circuit quantum electrodynamics.