Data in real world are usually characterized in multiple views, including different types of features or different modalities. Multi-view learning has been popular in the past decades and achieved significant improvements. In this paper, we investigate three challenging problems in the field of incomplete multi-view representation learning, namely, i) how to reduce the influences produced by missing views in multi-view dataset, ii) how to learn a consistent and informative representation among different views and iii) how to alleviate the impacts of the inherent noise in multi-view data caused by high-dimensional features or varied quality for different data points. To address these challenges, we integrate these three tasks into a problem and propose a novel framework termed Noise-aware Incomplete Multi-view Learning Networks (NIM-Nets). NIM-Nets fully utilize incomplete data from different views to produce a multi-view shared representation which is consistent, informative and robust to noise. We model the inherent noise in data by defining the distribution Γ and assuming that each observation in the incomplete dataset is sampled from the distribution Γ. To the best of our knowledge, this is the first work to unify learning the consistent and informative representation, alleviating the impacts of noise in data and handling the view-missing patterns in multi-view learning into a framework. We also first give a definition of robustness and completeness for incomplete multi-view representation learning. Based on NIM-Nets, we present joint optimization models for classification and clustering, respectively. Extensive experiments on different datasets demonstrate the effectiveness of our method over the existing work based on classification and clustering tasks in terms of different metrics.