A new factor-based representation of implied volatility surfaces is proposed. The factors adequately capture the moneyness and maturity slopes, the smile attenuation, and the smirk. Furthermore, the implied volatility specification is twice continuously differentiable and well behaved asymptotically, allowing for clean interpolation and extrapolation over a wide range of moneyness and maturity. Fitting performance on S&P 500 options compares favorably with existing benchmarks. The benefits of a smoothed implied volatility surface are illustrated through the valuation of illiquid index derivatives, the extraction of the risk-neutral density and risk-neutral moments, and the calculation of option price sensitivities.