Supermassive black holes are the central engines of active galactic nuclei (AGN) and are thought to lie at the heart of many massive galaxies. It is currently uncertain, however, whether AGN exist in low-mass dwarf galaxies, and if they do, whether they are powered by intermediate-mass black holes (IMBHs)- a missing population of black holes with masses between 100 and 100,000 solar masses. I present here the results of a systematic search for IMBH candidates detected by the X-ray emission produced through the accretion of matter onto the central black hole. To constrain the black hole masses I used the fundamental plane of black hole accretion (FPBHA), a relation between radio and X-ray luminosities of an accreting black hole allowing to estimate its mass. In my sample of ten nearby low-mass dwarf galaxies I have identified one strong IMBH candidate in the nucleus of NGC 404 with the mass of about 100,000 solar masses. Its mass, predicted by the FPBHA, agreed with many other published black hole mass estimates, conducted at different wavelengths using different methods. From established relations between the properties of active galaxies and their nuclei I found that the mass of the IMBH candidate in NGC 404 agreed with the prediction from relation between the nuclear black hole mass and the galaxy’s stellar mass and stellar velocity dispersion. I also present two multi-wavelength studies of ESO 243-49 HLX-1 (HLX-1), the strongest IMBH candidate currently known. In the first study I used the radio continuum and HI spectral line radio data to test the scenario in which HLX-1 is an X-ray nucleus of a stripped dwarf galaxy tidally disrupted by the passage through the disc of ESO 243-49. In the second study I analysed a combination of the X-ray, ultraviolet, optical and infrared data from the recurrent HLX-1 outbursts testing the hypothesis they were caused by an accretion-rate oscillation driven by wind instability in the inner part of the accretion disc.