The replacement of chemically inactive electrons by pseudopotentials is a common method used in many kinds of electronic structure calculations. Different fields (LCAO methods, plane wave-based methods, quantum Monte Carlo methods) have developed their own flavor of such potentials. According to the general theme of this book, the focus here is on the pseudopotentials used in plane wave calculations. The norm-conserving pseudopotential approach developed in the framework of plane wave calculations provides an effective and reliable means for performing calculations on complex molecular, liquid, and solid-state systems. In this approach only the chemically active valence electrons are dealt with explicitely. The inert core electrons are eliminated within the frozen-core approximation, being considered together with the nuclei as rigid non-polarizable ion cores. All electrostatic and quantum-mechanical interactions of the valence electrons with the cores, such as the nuclear Coulomb attraction screened by the core electrons, Pauli repulsion, and exchange and correlation between core and valence electrons, are accounted for by angular momentum-dependent pseudopotentials. These should reproduce the true potential and valence orbitals outside a chosen core region but remain much weaker and smoother inside. The valence electrons are then described by smooth pseudo orbitals which play the same role as the true orbitals, but avoid the nodal structure near the nuclei that keeps the core and valence states orthogonal in an all-electron framework. The Pauli repulsion largely cancels the attractive parts of the true potential in the core region, and is built into the therefore rather weak pseudopotential.