Multiview clustering aims to leverage information from multiple views to improve the clustering performance. Most previous works assumed that each view has complete data. However, in real-world datasets, it is often the case that a view may contain some missing data, resulting in the problem of incomplete multiview clustering (IMC). Previous approaches to this problem have at least one of the following drawbacks: 1) employing shallow models, which cannot well handle the dependence and discrepancy among different views; 2) ignoring the hidden information of the missing data; and 3) being dedicated to the two-view case. To eliminate all these drawbacks, in this work, we present the adversarial IMC (AIMC) framework. In particular, AIMC seeks the common latent representation of multiview data for reconstructing raw data and inferring missing data. The elementwise reconstruction and the generative adversarial network are integrated to evaluate the reconstruction. They aim to capture the overall structure and get a deeper semantic understanding, respectively. Moreover, the clustering loss is designed to obtain a better clustering structure. We explore two variants of AIMC, namely: 1) autoencoder-based AIMC (AAIMC) and 2) generalized AIMC (GAIMC), with different strategies to obtain the multiview common representation. Experiments conducted on six real-world datasets show that AAIMC and GAIMC perform well and outperform the baseline methods.