This thesis investigates the electronic structures of the rare earth 4f and actinide 5f materials using photoemission spectroscopy (PES) and Bremsstrahlung isochromat spectroscopy (BIS). These materials display interesting phenomena such as mixed valence and heavy-fermion properties. This is primarily due to the correlated f-electrons and their interaction with conduction electrons. The fundamental characterization of a many-body system is the spectral weight of the single-particle Green's function, which is determined by measuring the PES/BIS spectrum, the spectrum to remove and add electrons. For cerium materials, a unified understanding of the low-energy and 4f spectroscopic properties using the Anderson impurity Hamiltonian has been established in the last 10 years. In this picture, the low-energy properties are determined by a low-energy scale set by the Kondo temperature, which characterizes spin fluctuations. To test this picture quantitatively, a detailed examination of the $\alpha$-$\gamma$ transition in cerium has been undertaken in the framework of the Kondo volume collapse model using Anderson Hamiltonian parameters directly obtained from analyzing existing spectroscopic data. The results provide confirmation of the unified picture at a quantitative level not achieved before. For uranium materials, no such unified picture exists. The measured 5f spectrum does not resemble the cerium 4f spectrum, and only indirect evidence has been given for the applicability of the Anderson Hamiltonian. A complete set of PES/BIS measurements of the core-levels, valence band, and 5f states in the diluted alloy system Y$\sb{1-x}$U$\sb{x}$Pd$\sb3$ has been performed, and the results provide the first direct evidence that all uranium heavy-fermion spectra are to be understood in the framework of the Anderson Hamiltonian. With the aim of searching for the heavy-fermion bands, an angle-resolved PES measurement has been performed on URu$\sb2$Si$\sb2$. The results have major disagreements with band theory calculations. These include the observed quasi-two-dimensionality, the geometry of the Fermi surfaces, and the non-f band dispersion. A sharp dispersive peak with 50meV width at 50meV below the Fermi level is observed, and its lineshape is analyzed using Fermi liquid and marginal Fermi liquid theories.