In this thesis, I examine high and low frequency price discovery for US equity markets. In Chapter 3, I propose a methodology to disentangle high frequency price jumps into a permanent and transitory component. Using a variance decomposition and realized estimates I show that while jumps are extremely rare events, jump contribution to intraday price discovery is large. In Chapter 4, coauthored with Ryan Riordan, we examine the market dynamics of price jumps. We find that jumps have a predictable component which is captured by the degree of fragmentation in liquidity in minutes leading up to price jumps. Applying the methodology of Chapter 3, we show that fragmentation predicts noisier jumps. Lastly, in Chapter 5, co-authored with Evan Dudley, Luke Phelps and Ryan Riordan, we use mutual fund re sales to decompose low frequency quarterly stock prices into an efficient and noise component. We show that more than a quarter of variance in low frequency stock prices is attributable to noise. Overall, this thesis finds that noise is an important component of both high and low frequency stock price variation.