Updated: May 19, 2020
Tax-exempt accounts don't deliver a tax benefit when you contribute. You get future tax benefits; withdrawals at retirement are not subject to taxes. Since contributions into the account are made with after-tax dollars, there is no immediate tax advantage. The main advantage is that investment returns grow tax-free.
The most common is a tax-free savings account (TFSA).
If you contribute $5000 into a tax-exempt account today and the funds are invested in a mutual fund that provides a yearly 3% return, in 30 years the account would be valued at $12,135. When you take out the money at retirement, you won't pay taxes on any of it.