Thermoacoustic instability in turbulent combustors is a nonlinear phenomenon resulting from the interaction between acoustics, hydrodynamics, and the unsteady flame. Over the years, there have been many attempts toward understanding, prognosis, and mitigation of thermoacoustic instabilities. Traditionally, a linear framework has been used to study thermoacoustic instability. In recent times, researchers have been focusing on the nonlinear dynamics related to the onset of thermoacoustic instability. In this context, the thermoacoustic system in a turbulent combustor is viewed as a complex system, and the dynamics exhibited by the system is perceived as emergent behaviors of this complex system. In this paper, we discuss these recent developments and their contributions toward the understanding of this complex phenomenon. Furthermore, we discuss various prognosis and mitigation strategies for thermoacoustic instability based on complex system theory. © 2020 Author(s).