If one wants to understand how materials function, one should study their electronic structure near the Fermi level. The most direct way to do this is through angle-resolved photoelectron spectroscopy (“ARPES”), in particular through the combined use of tunable high-brilliance sources of soft x-rays and extreme ultraviolet radiation and highly efficient electron spectrometers with parallel detection of photoelectron emission angles and kinetic energies. Providing comprehensive information about band structures, Fermi surfaces, order parameters, and many-body effects, ARPES is now the standard technique for electronic structure, in much the same way as X-ray diffraction and inelastic X-ray or neutron scattering are standard techniques for lattice structure and dynamics. Yet, the development of ARPES continues. Important trends are to add time, spin, and spatial resolution and to systematically exploit the polarization degree of freedom of the incident radiation. Here, we will present state-of-the-art ARPES results and discuss some of these developments. The main focus will be on femtosecond time-resolved ARPES and its application on the chicken-and-egg problem of combined electron-lattice instabilities.
