I argue that one good reason for Scientific Realists to be interested in correspondence theories is the hope they offer us of being able to state and defend realistic theses in the face of well-known difficulties about modern physics: such theses as, that our theories are approximately true, or that they will tend to approach the truth. I go on to claim that this hope is unlikely to be fulfilled. I suggest that Realism can still survive in the face of these difficulties, as a claim about the kind of theories we want to aim for. I relate this conception of Realism to various contemporary discussions, both by realists and antirealists.