This thesis includes three self-contained essays on the threshold dynamics in onesector optimal growth models. In the Örst essay, we consider the preferences for wealth-habit in a one-sector optimal growth model. We show that the dynamics may encounter saddle-node bifurcations with respect to the parameters of the preferences. We analytically provide the monotone comparative statics and the continuity of the critical capital stock with respect to these parameters and the discount factor. In the second essay, we analyzed the joint dynamic implications of time-to-build lag in investment and non-convex technologies. We prove the existence of persistent cyclical dynamics even in one-sector optimal growth framework. Finally, in the third essay, considering time-to-build lag in non-classical optimal growth framework inducing threshold dynamics, we analyze the e§ects of an alternative information structure regarding the initial conditions on the equilibrium dynamics. In particular, we seek to understand the dependence of the cyclical dynamics on the information structure. In all essays, we also support the analytical solutions by numerical methods in order to better understand the underlying dynamics of the optimal path.