They were issued primarily by commercial banks in Canada and the United States before those countries created central banks in the early 20th century. These privately-issued bank notes ultimately failed to provide what the economy needed and so central banks were given this responsibility. The Bank of Canada has been issuing bank notes since 1935.
1 The cash you have in your wallets perfectly meets the three criteria of money. It is accepted almost everywhere, there’s very little counterfeiting, and the issuer – the central bank – won’t go bankrupt. We also target inflation, which means that the internal value of money is predictable.