Phase transitions and detailed magnetic properties of polycrystalline AP-YVO3.00(l) (prepared at ambient pressure by a conventional solid-state method) and polycrystalline HP-YVO3.04(1) and HP-YVO3.05(1) (AP-YV03 treated at 6 GPa and 1600 K during 130 and 15 min, respectively) were investigated. The three samples showed a remarkable exchange bias (EB) effect. HP-YVO3.04 and HP-YVO3.05 had similar chemical composition, crystallographic parameters, and particle size, but their magnetic properties were qualitatively different EB was negative at all temperatures in AP-YVO3 and HP-YVO3.05, resulting in the absence of magnetization reversal (MR). Positive EB was observed in HP-YVO3.04 between T-N2 = 71 K and T* = 88 K resulting in MR or negative magnetization between those temperatures. It was demonstrated that polycrystalline HP-YVO3.04 behaved similar to single crystals of YVO3+delta. By the careful control of the trapped magnetic field, measurement conditions were found under which no MR occurred in HP-YVO3.04 at moderate magnetic fields, indicating that MR is not an intrinsic property of YVO3+delta. A drastic effect of trapped magnetic fields on MR and memory effects were observed. The importance of an Insignificant" anomaly at T-FM = 140 K for MR was suggested. We also suggested that "positive exchange bias", "defects", "interfaces", and "pinning" should be keywords for understanding YVO3 and probably other perovslcite materials with the MR effect.