The pricing of corporate credit can be succinctly understood via the credit-implied volatility (CIV) surface. We invert it each month from the firm-by-maturity panel of CDS spreads via the Merton model, transforming CDS spreads into units of asset volatility. The CIV surface facilitates direct comparison of credit spreads at different "moneyness" (firm leverage) and time to maturity. We use this framework to organize the behavior of corporate credit markets into three stylized facts. First, CIV exhibits a steep moneyness smirk: Low leverage (out-of-the money) CDS trade at a large implied volatility premium relative to highly levered (at-the-money) CDS, holding all other firm characteristics fixed. Second, the dynamics of credit spreads can be described with three clearly interpretable factors driving the entire CIV surface. Third, the cross section of CDS risk premia is fully explained by exposures to CIV surface shocks. Using a structural model for joint asset behavior of all firms, we show that the shape of the CIV surface implies that aggregate asset growth is subject to stochastic volatility and severe, time-varying downside tail risk. Lastly, we explore CIV of other credit instruments including corporate bonds and sovereign CDS.