Where are Bitcoins stored?

As cryptocurrencies gain in popularity, the number of publicised hacks increases as well. Oftentimes the victims can’t do anything but watch as their tokens get lost forever. Apart from thefts and hacks like Mt Gox, users can lose their tokens due to computer failure and loss of devices or access keys.
Bitcoins are stored in digital wallets, which can be hardware-based (offline, also called cold wallets) or web-based (online, also called hot wallets). Digital wallets contain sets of private keys without which the bitcoin owner cannot access their currency.