Motivated by recent evolution of cutting-edge sensor technologies with complexvalued measurements, this chapter analyzes attack models and diagnostic solutions for monitoring industrial control systems against complex-valued cyber attacks. By capitalizing on the knowledge that the existing detection and closedloop estimation algorithms ignore the full second-order statistical properties of the received measurements, we show that an adversary can attack the system by maximizing the correlations between the real and imaginary parts of the reported measurements. Consequently, the adversary can pass the conventional attack detection methodologies and change the underlying system beyond repair. In the rest of the chapter, the first section surveys recent developments in secure closed-loop state estimation methodologies, and then reviews the fundamentals of complex-valued signals and their applications. The second section highlights the drawbacks of the state-of-the-art estimation methodologies and illustrates their vulnerability to cyber attacks. In the third section, we first review the existing attack models and then introduce the noncircular attack model. The fourth section surveys the state-of-the-art attack detection diagnostics and shows how to transform the cyber-attack detection problem into a problem of comparing statistical distance measures between probability distributions. The fifth section provides illustrative examples, followed by future research directions and conclusions.