This thesis studies the role of nonlinear environmental dynamics plays in determining the level and time profile of carbon taxes in different scenarios. In Chapter 1, I combine a standard neoclassical growth model with a state of the art carbon cycle model and compute the optimal taxes. In Chapter 2, I introduce temperature constraints to capture targets set by nations in the Paris Agreement and compute the new constrained optimal carbon taxes. In Chapter 1, I start with a standard neoclassical growth model for the world economy and combine with it a state-of-the art climate model; the climate model explicitly derives the nonlinear dynamics of the carbon cycle from physical laws, as opposed to the standard models with parameterized linear dynamics. This climate model captures nonlinear environmental dynamics that show how the timing and rate of emissions determines atmospheric concentrations of greenhouse gases in the atmosphere. Although such dynamics have been well known in environmental models, it was a challenge to include them in growth models with optimizing agents. I solve the model's nonlinear feedback effects by employing a new numerical solution technique. I found that the social cost of carbon in this framework was only slightly higher than what is estimated in standard models with linear dynamics. This paper provides a tractable formulation for a baseline model such that we can continue updating our environmental models to the best available science and make better policy recommendations. In Chapter 2, I consider the incorporation of temperature constraints into the above model to capture the Paris Agreement targets. After signing the Paris Agreement to limit the rise in global temperature within 2 C, countries are coming up with fiscal policies to limit their carbon emissions. Economic models should inform how to optimally implement these targets but so far have not because the Paris target is infeasible in the benchmark model. This paper challenges that in-feasibility by using the baseline model developed in Chapter 1. My model predicts higher benefits of rapid mitigation policies than the standard carbon cycles used in the literature, which makes the Paris target feasible. After showing the Paris target is feasible, I calculate the optimal taxes to achieve the target. I find that the carbon tax should be $298 in 2020 and should grow at 1.56% per year till 2050, after which it should decline at an average annual rate of 0.5% per year. I also show that capital taxes would be required along with carbon taxes to implement the optimal allocation. Given the state of policies around the world, most countries have much lower carbon taxes and there is a need to drastically increase the tax base and level to achieve the Paris Agreement targets.