[en] In this work, three members of the RERh${}_2$Si${}_2$ (RE = rare earth) series have been studied by means of UV and soft X-ray ARPES in combination with ab initio band structure calculations, XMLD and high resolution Compton scattering. Hereby, various aspects of the rich 4f physics in these rare-earth-based intermetallics have been highlighted, which include itinerant surface magnetism, Fermi surface folding across an antiferromagnetic phase transition and the Fermi surface crossover with temperature in a Kondo lattice. GdRh${}_2$Si${}_2$ is an antiferromagnet with alternating layers of ferromagnetically coupled Gd layers, which are separated by Si-Rh-Si buffers. Our combined UV-ARPES experiments and electronic structure calculations show that cleavage along a basal plane leaves behind either a Gd- or a Si-terminated surface, where the latter bears two distinct two-dimensional electron states (2DESs): a purely two-dimensional Shockley surface state and a Dirac-cone-type surface resonance. Both 2DESs at the Si-terminated surface couple via exchange interaction to the large Gd 4f moments buried below the topmost Si-Rh-Si trilayer and reveal a strong spin splitting with values up to ~185 meV in the Shockley state, when the magnetic ordering evolves. Our UV-ARPES and XMLD results suggest that both 2DESs play a decisive role in the mediation of the magnetic ordering at the surface, which first develops independently from the ordering in the bulk even far below the Néel temperature of 107 K, before it connects to the bulk magnetism at ~60 K. We further studied the influence of potassium deposition on the 2DESs by ARPES. In addition, our calculations suggest a small splitting of the Shockley surface state even in the paramagnetic phase and an unusual Rashba-like spin texture with a triple winding of the electron spins along the Fermi surface contour. However, in the present work this small splitting could not be resolved by the ARPES experiments due to the large lifetime broadening of the surface bands. The rest of this work takes a closer look at the bulk Fermi surface of the prominent heavy-fermion compound YbRh${}_2$Si${}_2$. We first established with the help of UV-ARPES measurements on EuRh${}_2$Si${}_2$, that the large Fermi surface in YbRh${}_2$Si${}_2$, which has previously been observed at low temperatures down to 1 K, indeed contains one additional hole per unit cell originating from the delocalized degree of freedom of the 4f hole in accordance with Luttinger’s Fermi surface sum rule, even though the Yb valence deviates only very slightly from Yb${}^{3+}$. This finding confirms, that the observed large Fermi surface in YbRh${}_2$Si${}_2$ is indeed a manifestation of a true many-body effect arising from strong electronic correlations. We have hereby made usage of the unique property of EuRh${}_2$Si${}_2$ being the only compound in the RERh${}_2$Si${}_2$ series with a divalent rare-earth ion. This offers the valuable opportunity to gauge experimentally and in the absence of strong renormalization effects on the electronic structure the topology and size of the large Fermi surface, which is expected for a nearly trivalent RERh${}_2$Si${}_2$ Kondo lattice. Upon entering the antiferromagnetic phase, the Fermi surface of EuRh${}_2$Si${}_2$ is subject to band folding, as observed by soft X-ray ARPES, due to the doubled size of the unit cell. This leads to a pronounced splitting and fragmentation of the Fermi surface, which could clearly be observed in the Fermi surface maps obtained by high-resolution UV-ARPES. In light of certain parallels between EuRh${}_2$Si${}_2$ and YbRh${}_2$Si${}_2$ concerning magnetic correlations, these findings might suggest that qualitatively similar changes of the Fermi surface topology upon entering the antiferromagnetic phase might also be of relevance for YbRh${}_2$Si${}_2$. This might have serious implications for the understanding of the enigmatic quantum phase transition in this compound and should certainly be taken into account. We have further addressed the long-standing problem of the temperature dependence of the Fermi volume in Kondo lattices. Theory predicts a crossover of the Fermi surface from large to small upon increasing temperature, as the 4f electron (or hole in Yb-based Kondo lattices) leaves the strong-coupling regime, where its degree of freedom is dissolved into the Fermi sea, and becomes effectively localized and decoupled from the conduction band. However, a comprehensive experimental proof of this prediction is still lacking to date. In this work, we have employed high-resolution Compton scattering to derive the EOND of YbRh${}_2$Si${}_2$, which can be viewed as the projection of the Fermi volume onto a two-dimensional plane in momentum space. Our measurements have indeed revealed pronounced changes in the EOND of YbRh${}_2$Si${}_2$ between 14 K and 300 K, which can be attributed to a reconstruction of the Fermi surface with increasing temperature. Comparison to equivalent measurements on YbCo${}_2$Si${}_2$, a reference system for the small Fermi surface, allowed us to conclude, that the YbRh${}_2$Si${}_2$ EOND at 300 K reflects a small Fermi surface, which results from a transition of the Fermi volume from large to small due to the temperature-driven breakdown of the Kondo lattice effect. To the best of our knowledge, this is the first experiment of this kind, which comprehensively visualizes the Fermi surface transition with temperature over the whole Brillouin zone in an Yb-based Kondo lattice.