Advanced visual interfaces, like the ones found in information visualization, intend to offer a view on abstract data spaces to enable users to make sense of them. By mapping data to visual representations and providing interactive tools to explore and navigate, it is possible to get an understanding of the data and possibly discover new knowledge. With the advent of modern data collection and analysis technologies, the direct visualization of data starts to show its limitations due to limited scalability in terms of volumes and to the complexity of required analytical reasoning. Many analytical problems we encounter today require approaches that go beyond pure analytics or pure visualization. Visual analytics provides an answer to this problems by advocating a tight integration between automatic computation and interactive visualization, proposing a more holistic approach. In this paper, we argue for Advanced Visual Analytics Interfaces (AVAIs), visual interfaces in which neither the analytics nor the visualization needs to be advanced in itself but where the synergy between automation and visualization is in fact advanced. We offer a detailed argumentation around the needs and challenges of AVAIs and provide several examples of this type of interfaces.