There have been numerous security breaches of TLS. The most famous was the Heart Bleed bug; basically if one knew where to look they could get a hold of the private keys. Once the private keys were known, they could authenticate and decrypt all the messages sent with this TLS type of security. There are also several TLS cipher suite downgrade attacks, such as Poodle, Freak, and Beast. These attacks trick the server into using a less secure cipher suite and then compromise the data. Additional information can be found online about these various attacks at https://vulnerablelife.wordpress.com/2015/03/07/the-most-brutal-security-bugs-freak-shellshock-poodle-heartbleed-and-beast/.