Plain English
Custodial means a third party (exchange, broker, app) holds your private keys and therefore your crypto. Non-custodial means you hold them. Almost every CEX is custodial; almost every self-managed wallet is non-custodial. “Not your keys, not your coins” is the shorthand.
How it actually works
In a custodial account, your balance is a database entry at the company. When you “withdraw,” they perform an on-chain transaction to send the actual crypto. While it sits there, they can freeze it, lose it, lend it, or have it seized by court order. In a non-custodial wallet, the private key lives on your device or hardware — only you can move funds, no help desk can help if you lock yourself out.
What it means for you
The right answer is almost always a mix. CEX for trading and on/off-ramp. Non-custodial for the position you actually want to hold. The HNW playbook usually splits further — some non-custodial in hot wallets for active DeFi, more in cold storage (hardware wallet or multisig) for the long-term core.
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Educational content only. Not investment, tax, or legal advice.