Memristor is an emerging non-volatile memory, which has several remarkable features such as simple structure, low power consumption, high integration density, and synaptic-like behaviour. Memristors have been primarily proposed to function as artificial synapses for constructing artificial neural network in the form of crossbar array. However, the crossbar array of memristors is confronted with severe potential path sneak currents issue, resulting in a large obstacle to further applications of memristors. In this paper, the causes of sneak currents issue in stacked crossbar array of memristor were analyzed briefly. The solutions, such as One Diode-One Resistor(1D1R), One Selector-One Resistor(1S1R), and One Transistor-One Resistor(1T1R), to suppress sneak currents were demonstrated. The promissing future of memristor with very large scale integrated crossbar array for various application was anticipated.