This paper describes a collection of multimodal corpora of referring expressions, the REX corpora. The corpora have two notable features, namely (1) they include time-aligned extra-linguistic information such as participant actions and eye-gaze on top of linguistic information, (2) dialogues were collected with various configurations in terms of the puzzle type, hinting and language. After describing how the corpora were constructed and sketching out each, we present an analysis of various statistics for the corpora with respect to the various configurations mentioned above. The analysis showed that the corpora have different characteristics in the number of utterances and referring expressions in a dialogue, the task completion time and the attributes used in the referring expressions. In this respect, we succeeded in constructing a collection of corpora that included a variety of characteristics by changing the configurations for each set of dialogues, as originally planned. The corpora are now under preparation for publication, to be used for research on human reference behaviour.