The routes to chaos and the global bifurcations leading to chaotic behavior are two fascinating areas of research in nonlinear dynamics. Chaotic dynamics are observed in a wide range of mathematical models across various disciplines of science and engineering. In recent years, the structural sensitivity of models with respect to their bifurcation structures leading to chaos has received increasing attention. The main objective of this talk is to discuss the structural sensitivity of the bifurcation structure associated with the classical Hastings–Powell model and the global bifurcations that give rise to chaotic regimes in the modified Lorenz system. A systematic bifurcation analysis, incorporating both local and global bifurcations, provides deeper insights into the routes to chaos and the nature of transient dynamics. The techniques discussed here can also be applied to problems arising in other areas of science and technology.