Previous work on predicting the target of visual search from human fixations only considered closed-world settings in which training labels are available and predictions are performed for a known set of potential targets. In this work we go beyond the state-of-the-art by studying search target prediction in an open-world setting. To this end, we present a dataset containing fixation data of 18 users searching for natural images from three image categories within image collages of about 80 images. In a closed-world baseline experiment we show that we can predict the correct mental image out of a candidate set of five images. In an open-world experiment we no longer assume potential search targets to be part of the training set and we also no longer assume that we have fixation data for these targets. We present a new problem formulation for search target recognition in the open-world setting, which is based on learning compatibilities between fixations and potential targets.