If I inherit my parent's stock portfolio, do I owe tax on all the gains they had?

Generally no, thanks to the step-up in basis. When you inherit appreciated assets like stocks or a house, your cost basis resets to the fair market value on the date of death. That wipes out the capital gains that built up during your parent's lifetime. If you sell soon after inheriting, you may owe little or no capital gains tax.

For example, if your parent bought shares for $20,000 and they were worth $120,000 at death, your basis becomes $120,000. Sell at $125,000 and you're taxed only on the $5,000 gain. Note that retirement accounts like traditional IRAs do not get a step-up; distributions are taxed as ordinary income. The IRS explains basis rules at irs.gov.