We utilise novel functional time series (FTS) techniques to characterise and forecast implied volatility in foreign exchange markets. In particular, we examine the daily implied volatility curves of FX options, namely; EUR-USD, EUR-GBP, and EUR-JPY. The FTS model is shown to produce both realistic and plausible implied volatility shapes that closely match empirical data during the volatile 2006-2013 period. Furthermore, the FTS model significantly outperforms implied volatility forecasts produced by traditionally employed parametric models. The evaluation is performed under both in-sample and out-of-sample testing frameworks with our findings shown to be robust across various currencies, moneyness segments, contract maturities, forecasting horizons, and out-of-sample window lengths. The economic significance of the results is highlighted through the implementation of a simple trading strategy.