Modelling the implied volatility surface (IVS) is fundamental for option pricing and for understanding the structure of volatility in financial markets. This work analyzed different approaches to IVS modelling, from classical models to machine learning techniques, including hybrid models that combine both paradigms. Daily data on SPX options provided by the CBOE were used, covering the period from 2009 to 2019. The main explanatory variables were log-moneyness and time to maturity, complemented, in the machine learning models, by the risk-free rate and a binary option-type indicator, to assess the additional contribution of these variables. All models followed the same training, tuning, and test process, ensuring comparability. Performance was evaluated using error metrics, such as R² and RMSE, complemented by residual analyses. The classical models — linear regression (OLS) and a fifth-degree polynomial model — highlighted the nonlinear nature of the IVS, whereas the cubic B-spline model achieved significant gains, though some residual structure remained unexplained. The machine learning techniques (Random Forest and XGBoost) showed substantial improvements in the metrics and almost eliminated residual structure, demonstrating a superior ability to adapt to complex patterns. The hybrid models, which apply machine learning to the spline model residuals, achieved results equivalent to or slightly better than those of the standalone machine learning models while preserving an interpretable foundation. This outcome confirms that integrating classical and machine learning models provides an effective balance between structure and flexibility, offering a robust framework for IVS modelling.