Here at Gemini we also offer wallet services to store BTC and ETH on Gemini — in short, every Gemini account has its own "wallet." If you click the Security’ link on the footer of any page on our site, you can learn more about our security design, and internal controls and procedures we have implemented to keep your funds safe and secure. You may also chose to leave funds on Gemini only while trading and remove them to a wallet of your choosing after you have completed your transaction.
If you'd like to transfer your digital assets to an external wallet or exchange, please navigate to the "Withdraw BTC" or "Withdraw ETH" page via the ‘Transfer Funds’ dropdown menu on the Gemini Dashboard. Once there, you'll be prompted to input a "Destination Address" (this is provided by your external wallet or exchange).