Whether or not your Social Security income is taxable depends on your total income, including your Social Security plus any other income. Generally speaking, if your only income is Social Security, you probably don't make enough money to be required to file a federal tax return.
For those with additional sources of income, the key figure is the Modified Adjusted Gross Income (MAGI). The MAGI includes half of your Social Security, plus other sources of income. Once your MAGI exceeds the base amount for your filing status ($32,000 for Married Filing Jointly or $25,000 for all others), at least part of your Social Security income becomes taxable. The taxable portion of your Social Security income increases once you reach additional MAGI thresholds.
At the state level, many states exempt Social Security from taxation, either partially or completely. Again, if your sole income is from Social Security, it's likely you don't need to file a state return either.
Enter your Social Security income into TurboTax, and we'll tell you if it's taxable.