This paper utilizes two methods to uncover the causality dynamic between the three leading cryptocurrencies: Bitcoin, Litecoin, Ripple, and nine major foreign currency markets. Firstly, we implement the technique of Diebold–Yilmaz to compute the spillover index between cryptocurrencies and currency markets. We find a significant return spillover effect between Bitcoin and Litecoin in the first three quarters of 2017. Still, the return spillover is merely meaningful in the first three quarters of 2015 for Ripple. However, the total volatility spillover index in the system decreases in the fourth quarter of 2017. Secondly, we apply the Bayesian graphical structural vector autoregressive estimations, and find that the current level of Bitcoin depends only on the previous level of the Chinese Yuan. The current level of Ripple strongly depends on the prior levels of Bitcoin, followed by Litecoin. The current level of Litecoin strongly depends on the previous level of Ripple, followed by the Chinese Yuan. These results indicate that there is a significant causal relationship among cryptocurrencies. However, except for the Chinese Yuan, major traditional currencies do not significantly affect cryptocurrencies.