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Recommender systems have been actively and extensively studied over past decades. In the meanwhile, the boom of Big Data is driving fundamental changes in the development of recommender systems. In this paper, we propose a dynamic intention-aware recommender system to better facilitate users to find desirable products and services. Compare to prior work, our proposal possesses the following advantages: (1) it takes user intentions and demands into account through intention mining techniques. By unearthing user intentions from the historical user-item interactions, and various user digital traces harvested from social media and Internet of Things, it is capable of delivering more satisfactory recommendations by leveraging rich online and offline user data; (2) it embraces the benefits of embedding heterogeneous source information and shared representations of multiple domains to provide accurate and effective recommendations comprehensively; (3) it recommends products or services proactively and timely by capturing the dynamic influences, which can significantly reduce user involvements and efforts.