The design of complex engineered systems is challenging, especially in early design stages due to the complex emergent behavior that often results in unforeseen failures. Emergent behavior is a distinctive aspect of systems in which the exhibited behavior of the system is more complex than the behavior of the individual components that shape the system. Understanding the emergent behavior is critical to perform an accurate assessment of the designed system. The objective of this paper is to explore the different existing concepts, methods, and approaches used by researchers to understand and manage emergent behavior in complex systems. We provide a critical review of the emergence concept to discern what characteristics about the causal process it reflects, so it can be used or implemented in further research in complex engineered systems. Specifically, this research explores the current state of-the-art on emergence, and identifies possible gaps in the research literature. We present different approaches used by engineers to deal with emergent behavior in different research areas such as Multiagent Systems (MAS), System of Systems (SOS), and Emergence Engineering.