Critical transitions are ubiquitous in natural, economic, and social systems, manifesting in the form of sudden changes to the state of the system when the system parameters are varied past a critical point. They often result in dangerous and catastrophic outcomes such as the collapse of ecosystems, epileptic seizures, and oscillatory instabilities in fluid mechanical systems. At the same time, some critical transitions are desirable, such as the onset of coherent lasing in lasers. We study critical transitions to explore universal features of such transition in diverse physical systems. We uncover the existence of a universal scaling relation during the critical transition to oscillatory instabilities in turbulent fluid mechanical systems. A phenomenon of spectral condensation, where the energy distributed over a broadband of frequencies in the power spectrum gets condensed into a dominant mode, is observed in fluid mechanical, optical and electronic systems. We define measures to quantify spectral condensation, and these measures follow inverse power law scaling with the peak power. The power-law relations are used to predict the amplitude of oscillations expected during oscillatory instabilities, which will help devise strategies to mitigate the high-amplitude oscillations in real-world systems. The second part of this work focuses on the effects of continuous variation of parameters on critical transitions. We compare the efficacy of various early warning signals in a thermoacoustic system exhibiting subcritical Hopf bifurcation and quantify the warning time obtained as a function of the parameter variation rate. We also experimentally demonstrate a mechanism of rate induced critical transition.