Quantization index modulation (QIM) techniques have been gaining popularity in the data hiding community because of their robustness and information-theoretic optimality against a large class of attacks. In this paper, we consider detecting the presence of QIM hidden data, which is an important consideration when data hiding is used for covert communication, or steganography. For a given host distribution, we are able to quantify detectability compactly in terms of a parameter related to the robustness of the hiding scheme to attacks. Using detection theory we show that QIM quickly transitions from easily detectable to virtually undetectable as this parameter varies. We also obtain performance benchmarks for QIM hiding in images, indicating that a scheme designed to be robust to, say, a moderate degree of JPEG compression, should be easily detectable. While practical application of detection theory to images is difficult because of statistical variations across images, we employ supervised learning to show that standard QIM schemes for images are indeed quite easily detectable. However, it remains an open issue as to whether it is possible to devise QIM variants that are less vulnerable to steganalysis.