Review assignment is a common task that many people such as conference organizers, journal editors, and grant administrators would have to do routinely. As a computational problem, it involves matching a set of candidate reviewers with a paper or proposal to be reviewed. A common deficiency of all existing work on solving this problem is that they do not consider the multiple aspects of topics or expertise and all match the entire document to be reviewed with the overall expertise of a reviewer. As a result, if a document contains multiple subtopics, which often happens, existing methods would not attempt to assign reviewers to cover all the subtopics; instead, it is quite possible that all the assigned reviewers would cover the major subtopic quite well, but not covering any other subtopic. In this paper, we study how to model multiple aspects of expertise and assign reviewers so that they together can cover all subtopics in the document well. We propose three general strategies for solving this problem and propose new evaluation measures for this task. We also create a multi-aspect review assignment test set using ACM SIGIR publications. Experiment results on this data set show that the proposed methods are effective for assigning reviewers to cover all topical aspects of a document.