In the present thesis the combination of real-time electricalmeasurements on nano-sampleswith simultaneous examination by transmission electron microscope (TEM) is discussed. Application of an electrical current may lead to changes in the samples thus the possibility to correlate such changes with the corresponding I-V measurements is very important. Using the TEMalong with in-house built sample holder and measurement setup, some important results were obtained. Firstly, current induced grain growth in polycrystalline Pt nanobridges (14 nm thick, 200 nm wide and 300 nm long) was investigated. Direct correlation was found between the evolution of the grain size and the change in the resistance. Secondly, the electromigration in Pt and Pd nanobridges was studied by in situ TEM technique. The material transfer during direct and reverse EM process in Pd bridges with different geometry was followed in-situ using scanning TEM. Further, the results of application of the Helium Ion Microscope (HIM) as a sculpting tool for nano-scaled samples are presented. We discuss the possibility to combine modification of the sample by the focused heliumion beam with local heating of the specimens. Heating is facilitated by using MEMS based heaters developed in-house. The detailed analysis of the modified samples was carried out with FEI Titan transmission electron microscope (TEM) operated at 300 kV. With the proposed method it is also possible to carry out the electrical measurements on a wide range of materials such as metallic and semi-conductor nanowires, nanobridges, nanopatricles and novel materials such as graphene.