This article studies a new problem of data stream clustering, namely, multiview data stream (MVStream) clustering. Although many data stream clustering algorithms have been developed, they are restricted to the single-view streaming data, and clustering MVStreams still remains largely unsolved. In addition to the many issues encountered by the conventional single-view data stream clustering, such as capturing cluster evolution and discovering clusters of arbitrary shapes under the limited computational resources, the main challenge of MVStream clustering lies in integrating information from multiple views in a streaming manner and abstracting summary statistics from the integrated features simultaneously. In this article, we propose a novel MVStream clustering algorithm for the first time. The main idea is to design a multiview support vector domain description (MVSVDD) model, by which the information from multiple insufficient views can be integrated, and the outputting support vectors (SVs) are utilized to abstract the summary statistics of the historical multiview data objects. Based on the MVSVDD model, a new multiview cluster labeling method is designed, whereby clusters of arbitrary shapes can be discovered for each view. By tracking the cluster labels of SVs in each view, the cluster evolution associated with concept drift can be captured. Since the SVs occupy only a small portion of data objects, the proposed MVStream algorithm is quite efficient with the limited computational resources. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed method.