Discovery of high-temperature superconductors aroused a great interest in studies on these materials. In 1987 an yttrium-based compound YBCO (Yttrium-Barium- Copper-Oxide) was synthesised with Tc at 93 K. It was immediately evident that the BCS theory does not explain the pairing mechanism in these oxide-based superconductors, which predicted that a maximum Tc of about 30 K could be achieved. Layered copper oxides were for a long time the most studied high-Tc superconductors. With the discovery, at the beginning of 2008, by Kamihara of a new non-cuprate high-Tc superconductor a different path of studies had opened. This family of quaternary oxyarsenides LaO1-xFxFeAs was surprising due to the presence of Fe, which should lead to long-range magnetic order suppressing superconductivity. Although the parent compound LaFeAsO is not superconducting, electron doping (by partial substitution of O2- with F-) leads to superconductivity with Tc of 26 K. Since these discoveries there has been extensive research on the family of rare-earth quaternary oxypnictides with general formula REFaAsO (RE = La, Sm, Ce, Nd, Pr, Gd, Tb, Dy) and with Tc reaching 55 K for electron doped SmFeAsO. A study of new NdFeAsO family with Sr doping on Nd site was conducted. Synthesis of Nd1-xSrxFeAsO compounds and their further characterisation revealed that hole doping in these materials is a successful route to achieve superconductivity. Partial substitution of Nd3+ by Sr2+ with small doping level (x = 0.05) shows semiconducting type behaviour, while increasing doping level leads to the emergence of metallic conductivity and with level of doping 20% obtaining superconductivity at Tc = 13.5 K. These materials adopt a simple tetragonal crystal structure (space group P4/nmm), which undergoes a structural phase transition on cooling to orthorhombic symmetry (space group Cmma). The changes of structural, electronic and magnetic properties with doping level show very different behaviour – non-symmetric to the electron doped side of the phase diagram. The family of Fe-As based superconductors has expanded further by the discoveries of A1-xA’xFe2As2 (A = Alkaline Earth, A’ = Alkali metal), LiFeAs and NaFeAs phases, Sr3Sc2Fe2As2O5. A series of iron-based oxyarsenides with general formula Sr4M12O6M2 2As2 (M1 = Sc, Cr, V; M2 = Fe, Co, Ni) was synthesised and their structure was studied using powder X-ray and neutron diffraction. These materials adopt tetragonal crystal structure (space group P4/nmm) in analogy with REFeAsO systems. The Fe-As planes are sandwiched between perovskite K2NiF4-type oxide layers of Sr4M2O6 (MI = Sc, Cr, V), the large size of which creates a large distance between Fe-As planes. In spite of structural analogy with REFeAsO these new materials show a different behaviour from REFeAsO, which is absence of a structural phase transition on cooling. Both Sr4V2O6Fe2As2 and Sr4Sc2O6Ni2As2 compounds are superconducting without doping with Tc at 28 K and 2.5 K respectively. Neither Sr4Sc2O6Fe2As2 nor Sr4Cr2O6Fe2As2 show these properties, but are good parent compounds for doping, which may lead to producing compounds that achieve superconductivity. Further research was made with synthesising doped Sr4Cr2O6Fe2As2 with doping on Fe site with Co. The structure and magnetic and electrical properties of these compounds were studied and proved to show superconducting behaviour with Tc up to 17.5 K for 5% Co doping.