The discovery of high-temperature conventional superconductivity in H3S with a critical temperature of Tc=203 K was followed by the recent record of Tc ~250 K in the face-centered cubic (fcc) lanthanum hydride LaH10 compound. It was realized in a new class of hydrogen-dominated compounds having a clathrate-like crystal structure in which hydrogen atoms form a 3D framework and surround a host atom of rare earth elements. Yttrium hydrides are predicted to have even higher Tc exceeding room temperature. In this paper, we synthesized and refined the crystal structure of new hydrides: YH4, YH6, and YH9 at pressures up to 237 GPa finding that YH4 crystalizes in the I4/mmm lattice, YH6 in Im-3m lattice and YH9 in P63/mmc lattice in excellent agreement with the calculations. The observed very high-temperature superconductivity is comparable to that found in fcc-LaH10: the pressure dependence of Tc for YH9 also displays a dome like shape with the highest Tc of 243 K at 201 GPa. We also observed a Tc of 227 K at 237 GPa for the YH6 phase. However, the measured Tcs are notably lower by ~30 K than predicted. Evidence for superconductivity includes the observation of zero electrical resistance, a decrease of Tc under an external magnetic field and an isotope effect. The theoretically predicted fcc YH10 with the promising highest Tc>300 K was not stabilized in our experiments under pressures up to 237 GPa.