We model the dynamic competition among national fiat currencies, cryptocurrencies, and Central Bank Digital Currencies (CBDCs), whereby countries strategically digitize their currency and launch CBDC in response to competition from emerging cryptocurrencies and other currencies. Countries with strong but non-dominant currencies benefit the most from launching CBDC early on. The country with the strongest currency has relatively high incentives to digitize its currency so as to nip cryptocurrency growth in the bud and to counteract competitors' CBDCs. We also study the role of stablecoins in currency competition, as well as the effects of currency competition and cryptocurrencies on financial innovation. Our findings help rationalize recent developments in currency and payment digitization, while providing insights into the battle of currencies and the future of money.