The transfer itself is not taxable or reported. However, you need to know the cost basis of the stocks, because that will determine your capital gains when you sell them. Cost basis is generally what your spouse paid for the stocks when they bought them, but it might be adjusted due to mergers, stock splits, and other activities. You may be able to get the basis from the stock broker, if you can provide details of the transfer, such as your spouse's account number. If the stocks were transferred from your spouse's account to your account within the same broker, the broker may have also kept track of the basis for you, but I suggest calling them to verify this.
If your spouse sold stocks to purchase other stocks, the gain or loss would be reported on your spouse's tax return and you don't have to worry about that.
