With a non-custodial wallet, you are in control of your private keys [these private keys control your cryptocurrency] and they prove that the funds on the blockchain belong to you.

If you are using a custodial wallet then someone else is in control of your private keys. Examples of custodial wallets are most of the traditional web-based exchanges e.g. Coinbase, Kraken, Binance etc.. In the past there have been many examples of exchanges being hacked or closed down e.g.

• Mt. Gox - Exchanged hacked in 2011 - around 850,000 bitcoin stolen!

• QuadrigaCX - Owner died in 2018 - over 26,000 bitcoin lost!

• Bitfinex - Exchange hacked in 2016 - lost 120,000 bitcoin!

[See a full list here - https://bringbackmycrypto.com/blog/exchangehacks ]

Custodial wallet are often considered less secure than a non-custodial wallet, however you may prefer to use a custodial wallet because they are convenient and do not require much responsibility on your behalf.

Using a non-custodial wallet means you are now responsible for securing your wallet e.g. backing it up and/or password protecting it. Many of the non-custodial wallets (called HD Wallets) today also offer an additional level of security in the form of a seed phrase (sometimes called a pass phase) - this is a series of 12, 18 or 24 words that are created by the wallet at setup. Remembering these words, in the correct order, will enable you to recreate your wallet complete with all your funds.

Examples of well known non custodial wallets are:

Bitcoin core, Wasabi, Electrum, Blue Wallet, Trezor, Ledger, Exodus.

WARNING: There are many fake wallets out there - so make sure you download your wallet from the companies website and it is also not advisable to buy second hand hard wallets like Trezor or Ledger. [e.g. Avoid buying hardware wallets on ebay or Amazon]