Plane waves (PW) represent the standard basis-set choice in solid-state chemistry, implying periodicity by construction and enabling the efficient computation of electrostatic interactions by fast Fourier transformation (FFT) techniques. Linked to intrinsic periodicity is however the major disadvantage of non-locality, representing a challenge when it comes to describing local fluctuations of the electronic density at the core or when tackling systemspecific local features like defects or local charges. Mixed or augmented approaches, that combine plane waves with local basis sets, have therefore been developed extensively, enabling to exploit the advantages of both representations. Mixed schemes expand the global density using both intrinsically periodic plane waves and atom-centered local basis functions, such as Gaussian 1 or numerical orbitals. Doing so, the Gaussian and plane wave (GPW) method enables to still evaluate Coulomb and exchange correlation (XC) contributions efficiently using FFT, while sparsity of the density matrix can be exploited for contributions of kinetic energy and electron-nuclei interaction. In consequence, Kohn-Sham matrix build up in GPW scales linearly with system size, which has to be compared with the typical quadratic scaling of PW codes. However, relying on global densities only, GPW has to replace core electrons with pseudo potentials: The plane wave representation is sufficiently accurate for feasibly small energy cutoffs when dealing with smooth electron densities in interatomic regions. The description of the heavily oscillating density at the atomic cores would require impracticably high thresholds if not relying on pseudo potentials. The latter however hinder all-electron computations and thus the modeling of core excitations in e.g. X-ray, nuclear magnetic or electron paramagnetic resonance (NMR or EPR) spectroscopy. Furthermore, in the case of second-row transition metals, it might be necessary to consider localized semi-core states in the explicitly treated valence region, requiring high cutoffs for state-of-the-art norm-conserving pseudo potentials. Augmented plane wave (APW) approaches therefore combine a dual basis-set representation with the standard strategy to divide the system into two regions, an interatomic region, which is still relying on plane waves, and core regions, which are in contrast represented by localized basis sets. Within the extensive research field of APW methods, the projector augmented wave (PAW) method by introduced the general idea to rely on a linear transformation between pseudo and all-electron wave functions based on projection operators, ensuring that the relevant ground-state or excited-state equations can be reformulated within the auxiliary basis sets, while still expanding integrals over all space. Using projection operators enables to separate the hard local atomic densities from the soft smoothly decaying global density.