Computer architecture has been undergoing a revolution with increasing prevalence of heterogeneous, specialized, and massively-parallel hardware systems, to accelerate major data-intensive workloads and enable better system scaling. Hardware for novel computing paradigms (e.g., processing in memory, quantum computing) is already being prototyped and commercialized, and system complexity is increasing. At the same time, hardware security issues at the very low levels have been causing great concern and threatening the benefits and future of even old computing paradigms like speculative execution and main memory (DRAM) scaling. We are at an exciting time when the tensions between low-level architecture/technology innovations and system security problems such innovations expose are being heavily examined and such tensions are likely to increase for the foreseeable future. In this talk, we will examine the interplay between computer architecture and system security in modern and emerging computing systems. We will cover major trends in computer architecture and discuss how they may impact hardware and system security. We will examine potential threats as we see them, especially in areas related to the memory hierarchy and data access. We will also examine the requirements security goals may demand from future hardware architectures and technologies. We aim to provide directions that we believe would be fruitful and important to study to proactively address security challenges of emerging hardware architectures and design fundamentally-secure computing systems.