On behalf of the Radioastron pulsar group this report presents an overview of the studies which were done with the Radioastron space radio telescope during the first four years of mission operation, including the early and key science programs. Space-VLBI observations of pulsars with the highest angular resolution revealed the new interstellar plasma scattering effects, such as, resolving the substructure in the scattering disk. Diameters of scattering disks were measured for several pulsars and the distances to the effective scattering screens were estimated. Layers of scattering plasma were detected to be located relatively close to the Sun (10-100 pc). Such layers might be responsible for fast flux variations of compact extragalactic radio sources. A new insight on the interstellar scattering was demonstrated by study of the instantaneous visibilities which were measured with the Space-VLBI observations of giant pulses from the Crab pulsar.