In the global era of knowledge economy and electronic information, semiconductor memories play a crucial role in the storage of the massive information. In order to achieve a higher integration density, the microelectronics process node is pushed forward to the next generation according to the Moores Law. However, the current mainstream nonvolatile memory technology based on charge storage, such as flash memory, is rapidly running into its physical limit due to the tradeoffs between the high speed, long time retention and low power operation. Therefore, several new types of nonvolatile memories based on other storage concepts have been intensively investigated to replace Flash. Resistive random access memory (RRAM) device, which is based on resistance change modulated by electrical stimulus, has been considered as one of the most promising candidate for next-generation nonvolatile memory due to its potential advantages for simple structure, fast switching speed, excellent scalability, three-dimensional (3D) stackable integration, and good compatibility with the current complementary metal oxide semiconductor (CMOS) technology. However, a crossbar array consisting of only RRAM cell suffers unavoidable cross-talk interference due to leakage current paths through neighboring unselected cells with low resistances, leading to a misreading problem, the biggest hindrance for the high-density memory application. It can be effectively tackled by the addition of necessary nonlinearity to the RRAM by integrating a highly non- linear and bidirectional selector device. In this paper, we give an overview on the familiar architectures to diminish the sneak current in crossbar array, including 1D1R (one diode one resistor), 1S1R (one selector one resistor), 1CRS1R (one CRS device one resistor, complementary resistive switch (CRS) devices forming by two back-to-back connected memory cells) and 1R (one resistor) with self-rectifying effect. In the meantime, we discuss the research trends and the challenges of high-density storage based on RRAM passive cross-array. Finally, future research direction and prospects, as well as main challenges awaiting RRAM high-density memory are given. The application of diodes with large forward current density, high rectification ratio, low preparation temperature and easy 3D integration are the key to achieve high density in 1D1R structure integration. It is of great significance to find materials with better performance and applicability, and to carry out theoretical research on the integrated applications of 1S1R and 1CRS1R structures. Since the 1R with self-rectifying effect is simpler and more cost-effective than other integrated structures, further research to clarify intrinsic physical mechanism of 1R, and develop high-performance self-rectifying RRAM devices with large rectification ratio, high current density, uniformity, stability, and reliability are the significant processes to the achievement of RRAM high-density storage applications.