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Field emission (FE) is defined as the emission of electrons from the surface of a condensed phase (metal or semiconductor) into another phase, usually a vacuum, under the action of high electrostatic field. Detailed description of theory of electron emission from metallic and semiconducting materials, as well as required measurement techniques are presented in this work. Description of mutual shielding effect, which is an important issue for cold cathode applications, and an overview of electro-thermal properties of carbon nanotubes and metallic nanowires can be find as well. Experimental part of the work is focused on results of comprehensive FE investigations of different materials suitable for cold cathodes applications, as well as on investigation of origins of a parasitic FE from Nb surfaces and photocathodes required for electron accelerators like the European X-ray free-electron laser (XFEL). Detailed description of a newly developed scanning anode FE microscope (SAFEM) can be found, too. The SAFEM was developed within this work and will be regularly used to ensure low parasitic FE from the actual photocathodes in the electron gun of the XFEL.