The article reviews the quantum properties of low-capacitance Josephson junction devices, focusing on their potential as qubits in quantum information processing. The relevant quantum degrees of freedom are Cooper pair charges on small islands or fluxes in ring geometries, both near degeneracy points. The coherence of the superconducting state is exploited to achieve long phase coherence times. Single- and two-qubit quantum manipulations can be controlled by gate voltages or magnetic fields, methods established for single-charge systems or SQUID technology. Recent experiments have demonstrated coherent oscillations in Josephson charge qubits, displaying the laws of quantum mechanics in solid-state devices. The article also discusses the challenges of quantum measurement, including the use of single-electron transistors (SETs) for reading out the quantum state of a qubit. The measurement process is analyzed through the time evolution of the density matrix of the coupled system, considering the dissipative effects introduced by the SET. The article concludes with a discussion of the potential applications of Josephson qubits in quantum computing and the theoretical concepts of quantum logic gates and algorithms.The article reviews the quantum properties of low-capacitance Josephson junction devices, focusing on their potential as qubits in quantum information processing. The relevant quantum degrees of freedom are Cooper pair charges on small islands or fluxes in ring geometries, both near degeneracy points. The coherence of the superconducting state is exploited to achieve long phase coherence times. Single- and two-qubit quantum manipulations can be controlled by gate voltages or magnetic fields, methods established for single-charge systems or SQUID technology. Recent experiments have demonstrated coherent oscillations in Josephson charge qubits, displaying the laws of quantum mechanics in solid-state devices. The article also discusses the challenges of quantum measurement, including the use of single-electron transistors (SETs) for reading out the quantum state of a qubit. The measurement process is analyzed through the time evolution of the density matrix of the coupled system, considering the dissipative effects introduced by the SET. The article concludes with a discussion of the potential applications of Josephson qubits in quantum computing and the theoretical concepts of quantum logic gates and algorithms.