In this chapter, we start first by presenting some typical properties of the local volatility surface, namely: the At-The-Money volatility, skew and curvature. We then move on to the implied volatility dynamics embedded in the local volatility model. We introduce the dynamic of the smile through the Skew Stickiness Ratio (SSR ratio) and lay out a methodology for its computation. The end of the chapter is devoted to the P&L explanation process and the testing of its underlying assumptions (i.e. Delta and Vega hedged positions) through well-chosen scenarios.