One of the most surprising tax bills in equity compensation comes from the alternative minimum tax, or AMT. It can arrive in a year when you haven't sold anything and haven't received any cash.
AMT is a parallel tax calculation meant to ensure higher earners pay at least a minimum amount of tax. Your tax is figured both ways, under the regular rules and under the AMT rules, and you pay whichever is higher. AMT rates are generally 26% or 28%, depending on income.
When you exercise ISOs and still hold the shares at the end of that calendar year, the spread, the difference between your strike price and the fair market value on the day you exercised, counts as income for AMT purposes. No shares were sold and no cash changed hands, but the spread can still create a real tax bill.
If you exercise and sell in the same calendar year, the sale is a disqualifying disposition. The spread is taxed as ordinary income instead, and the AMT adjustment generally doesn't apply to those shares.
Say you exercise 10,000 ISOs with a $2 strike price when the shares are worth $20. The spread is $180,000. For regular tax, that isn't income yet. For AMT, it is. Depending on the rest of your income, that can mean a significant tax bill for the year you exercised.
AMT paid because of ISO exercises can create a credit that may reduce your regular tax in future years. Recovering it can take time and depends on your future tax situation, so it isn't a reason to ignore the bill up front.