This paper reviews researches on quantum oracle computations when oracles are not perfect, i.e., they may return wrong answers. We call such oracles biased oracles, and discuss the formal model of them. Then we provide an intuitive explanation how quantum search with biased oracles by Høyer, et al.(2003) works. We also review the method, by Buhrman, et al.(2005), to obtain all the answers of a quantum biased oracle without any overhead compared to the perfect oracle case. Moreover, we discuss two special cases of quantum biased oracles and their interesting properties, which are not found in the classical corresponding cases. Our discussion implies that the model of quantum biased oracle adopted by the existing researches is natural.