Some drives conform to higher ATA standards than others. An ATA secure wipe (if available) will tell the controller to "release the charge in the NAND chips", effectively making it appear that there is no data on the drive. This can brick drives, as some overwrite firmware as well.
More importantly, a study done by the University of California San Diego showed that an ATA secure erase command may not sufficiently destroy data: http://nvsl.ucsd.edu/index.php?path=projects/sanitize
Some older consumer SSDs (and some newer ones) are SEDs, or Self Encrypting Drives. Each write to drive is first passed though the drive's controller which encrypts data before it is written. The advantages of these types of drives is that by changing the key used for encryption, one can have some level of confidence that the data is not recoverable. Data is unrecoverable by consumers.
As others have pointed out, with SSDs, there are other "reserve" blocks of memory which do not tend to be overwritten when preforming a disk wipe (especially generic disk wipes). This again should not be of significant worry for consumers as consumer level disk recovery software would be unable to recover from those special blocks.