Thermoacoustic instability is a plaguing problem in confined combustion systems, where self-sustained periodic oscillations of ruinous amplitudes that cause serious damage and performance loss to propulsive and power generating systems occur. In this chapter, we review the recent developments in understanding the transition route to thermoacoustic instability in gaseous combustion systems and describe a detailed methodology to detect this route in a two-phase flow combustion system. Until now, in these combustion systems, the transition to such instabilities has been reported as Hopf bifurcation, wherein the system dynamics change from a state of fixed point to limit cycle oscillations. However, a recent observation in turbulent gaseous combustion system has shown the presence of intermittency that precedes the onset of thermoacoustic instability. Intermittency is a dynamical state of combustion dynamics consisting of a sequence of high amplitude bursts of periodic oscillations amidst regions of relatively low amplitude aperiodic oscillations. Here, we discuss the process of transition to thermoacoustic instability in the two-phase flow system due to change in the control parameter, a location of flame inside the duct. As the flame location is varied, the system dynamics is observed to change from a region of low amplitude aperiodic oscillations to high amplitude self-sustained limit cycle oscillations through intermittency. The maximum amplitude of such intermittent oscillations witnessed during the onset of intermittency is much higher than that of limit cycle oscillations. We further describe the use of various tools from dynamical systems theory in identifying the type of intermittency in combustion systems.