Causal relationships are at the heart of the scientific method. The causal revolution of the 21st century has opened the doors for many new approaches to quantify such relationships. In this thesis, we study the novel framework of proximal causal inference, which enables estimation of causal parameters even in the presence of unmeasured confounders, overcoming the limitations imposed by the Conditional Exchangeability assumption of the classic causal framework. In particular, we shall focus on determining and estimating the Causal Exposure Response Function (CERF) under this new set of assumptions. First, we introduce the problem and present a literature review of existing approaches to estimate bridge functions; then, we show theoretical results for extensions of classic linear results and a novel quasi- Bayesian method. This is then completed by showcasing performance on many simulated numerical examples and two real-world problems: Sustainable Causal Investing, and the effect of exercise on sleep.