In this paper, we analyze the collision resistance of SHA-2 and provide the first results since the beginning of the NIST SHA-3 competition. We extend the previously best known semi-free-start collisions on SHA-256 from 24 to 32 (out of 64) steps and show a collision attack for 27 steps. All our attacks are practical and verified by colliding message pairs. We present the first automated tool for finding complex differential characteristics in SHA-2 and show that the techniques on SHA-1 cannot directly be applied to SHA-2. Due to the more complex structure of SHA-2 several new problems arise. Most importantly, a large amount of contradicting conditions occur which render most differential characteristics impossible. We show how to overcome these difficulties by including the search for conforming message pairs in the search for differential characteristics.