We review some recent spectroscopic results on low-dimensional systems, including high-T-c superconductors, and charge density wave compounds. We briefly discuss the reasons for the present interest in these materials, and the relevance of band mapping experiments by angle-resolved photoemission spectroscopy. The main focus of the paper is on high-energy resolution, which can be exploited to probe the quasiparticle excitations, and to study the characteristic instabilities of the Fermi surface. Gap spectroscopy in the ordered phases is a prominent part of this research, namely in the cuprates. The normal state properties, however, are often as interesting. This is particularly true in 1D, where the photoemission results indicate strong deviations from a Fermi liquid scenario. (C) 1999 Elsevier Science B.V. All rights reserved.