Abstract: The dynamics of financial prices emerge from the interaction of thousands of trading algorithms operating across multiple time scales. From an options trader’s perspective, option prices act as experimental probes of this complex system. Starting with Bachelier and Black-Scholes, we show why constant-volatility models fail to explain empirical features such as volatility clustering, leverage, and the persistent shape of implied volatility surfaces. Stochastic volatility models capture many of these features; rough volatility is then motivated by power-law scaling in volatility dynamics. The talk concludes with quadratic rough Heston fits to SPX and VIX smiles, illustrating how rough volatility provides a coherent framework for pricing and risk management.