Kraken is an exchange, not a wallet service. We provide clients the ability to deposit funds to our corporate wallet for safekeeping while the funds are being exchanged or used for trading or staking, but we do not provide a personal wallet service.
As with most exchanges, funds sent to deposit addresses are moved to cold storage and hot wallets. Withdrawals are handled by the hot wallet and not the deposit address; the sending address for withdrawals will be different than the deposit address.
Do not attempt to withdraw digital assets from Kraken if ownership of the sending address is relevant to the transaction.
For example, if you're depositing into an Initial Coin Offering (ICO) address, Kraken's hot wallet will be the depositor and not your personal Kraken deposit address. You will not be able to receive those ICO tokens.
What wallets are there?
While we do not recommend any particular wallets, hardware wallets do a great job of balancing usability with security for most mainstream clients.
Ledger and Trezor are two of the most popular makers of hardware wallets. You can visit the websites below to learn more about these security devices.