This thesis is a review of five publications, where small and medium-sized (N ≤ 102) aluminum and sodium clusters and their electronic structure are studied using a first-principles simulation method. The initial motivation for these studies was to explain the complicated pattern of measured ionization potentials of small aluminum clusters, which deviates considerably from the corresponding behaviour of alkali clusters. It became evident that in order to explain the experimental results it was necessary to take into account the cluster temperature in the experiments. The effect of the temperature is to lower the ionization potential of the ionic ground state configuration via thermal vibrations of ions and isomerization. The problem was studied using molecular dynamics and so called generalized Koopmans' theorem, which in the density functional regime connects the ionization potential and the energy eigenvalue of the highest occupied single-particle state. Furthermore, the same formalism was applied to the ionization potentials of small sodium clusters, and most convincingly to the photoelectron spectra of aluminum cluster anions. In the case of aluminum cluster anions, the high sensitivity of the electronic spectrum to the geometrical structure allowed a structural assignment of the observed isomers in the experiments. The main part of this thesis concerns the physical and chemical properties of aluminum clusters. It is observed that the structure of aluminum clusters develops quite rapidly from the icosahedral stacking to the less strained (more or less distorted) decahedral and FCC-lattice based structures. Furthermore, the total shapes of the clusters obey in many instances the so called jellium model, where the positive background density of ions is replaced by a homogeneous charge density. The electronic structure of aluminum clusters evolves rapidly from the strong s - p hybridization to the jellium-like delocalized electronic density, which is perturbed by the crystal field effects caused by the specific geometry of the cluster. Indications of the metallization of aluminum clusters are observed as small energy gaps between the occupied and unoccupied single-particle states, when the cluster size is increased. The binding energies (i.e. the energy required to detach an atom) show a smooth and nearly monotonic increase towards the theoretical bulk value, which within this simulation method was exaggerated. The nearest neighbour distance of aluminum clusters approaches the true bulk value monotonically and rapidly.