The development and characterization of experimental setups for angle-resolved photoelectron spectroscopy (ARPES) and spin- and angle-resolved photoelectron spectroscopy (SARPES) is described. Subsequently, the two techniques are applied to studies of the electronic band structure in topologically non-trivial materials. The laser-based ARPES setup works at a photon energy of 10.5 eV and a typical repetition rate in the range 200 kHz to 800 kHz. By using a time-of-flight electron energy analyzer electrons emitted from the sample within a solid angle of up to ±15 degrees can be collected and analyzed simultaneously. The SARPES setup is equipped with a traditional hemispherical electron energy analyzer in combination with a mini-Mott electron polarimeter. The system enables software-controlled switching between angle-resolved spin-integrated and spin-resolved measurements, thus providing the possibility to orient the sample by mapping out the electronic band structure using ARPES before performing spin-resolved measurements at selected points in the Brillouin zone. Thin films of the topological insulators (TIs) Bi2Se3, Bi2Te3 and Sb2Te3 are grown using e-beam evaporation and their surface states are observed by means of ARPES. By using a combination of low photon energies and cryogenic sample temperatures the topological states originating from both the vacuum interface (surface) and the substrate interface are observed in Bi2Se3 films and Bi2Se3/Bi2Te3 heterostructures, with total thicknesses in the ultra-thin limit (six to eight quintuple layers), grown on Bi-terminated Si(111) substrates. Band alignment between Si and Bi2Se3 at the interface creates a band bending through the films. The band bending is found to be independent of the Fermi level (EF) position in the bulk of the substrate, suggesting that the surface pinning of EF in the Si(111) substrate remains unaltered after deposition of the TI films. Therefore, the type and level of doping of the substrate does not show any large influence on the size of the band bending. Further, we provide experimental evidence for the realization of a topological crystalline insulator (TCI) phase in the narrow-band semiconductor Pb1−xSnxSe. The TCI phase exists for temperatures below the transition temperature Tc and is characterized by an inverted bulk band gap accompanied by the existence of non-gapped surface states crossing the band gap. Above Tc the material is in a topologically trivial phase where the surface states are gapped. Thus, when lowering the sample temperature across Tc a topological phase transition from a trivial insulator to a TCI is observed. SARPES studies indicate a helical spin structure of the surface states both in the topologically trivial and the TCI phase. QC 20130507