As memory scales down to smaller technology nodes, new failure mechanisms emerge that threaten its correct operation. If such failure mechanisms are not anticipated and corrected, they can not only degrade system reliability and availability but also, perhaps even more importantly, open up security vulnerabilities: a malicious attacker can exploit the exposed failure mechanism to take over the entire system. As such, new failure mechanisms in memory can become practical and significant threats to system security. In this work, we discuss the RowHammer problem in DRAM, which is a prime (and perhaps the first) example of how a circuit-level failure mechanism in DRAM can cause a practical and widespread system security vulnerability. RowHammer, as it is popularly referred to, is the phenomenon that repeatedly accessing a row in a modern DRAM chip causes bit flips in physically-adjacent rows at consistently predictable bit locations. It is caused by a hardware failure mechanism called DRAM disturbance errors, which is a manifestation of circuit-level cell-to-cell interference in a scaled memory technology. We analyze the root causes of the RowHammer problem and examine various solutions. We also discuss what other vulnerabilities may be lurking in DRAM and other types of memories, e.g., NAND flash memory or Phase Change Memory, that can potentially threaten the foundations of secure systems, as the memory technologies scale to higher densities. We conclude by describing and advocating a principled approach to memory reliability and security research that can enable us to better anticipate and prevent such vulnerabilities.