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Very interesting question which can be answered in multiple perspectives.
Techniques: If you are looking at techniques in data modelling, there are quite a few that are exploding. Deep learning, spectral methods, kernel methods, probabilistic graphical models, social networking analytics are all the latest and fastest growing areas.
Business verticals: We are also seeing a lot of interest in data science applications in the entire circle of health care industries like pharmaceutical industries, hospitals and insurance companies. Previously only banks and retail organisations used to be analytics savvy. So, if I interpret your questions as what are the areas where data science is becoming a new approach to problem solving, I advise you to watch out the healthcare sector.
Horizontal problems: we often hear a lot from clients from a variety of verticals about their need to solve questions related to unstructured data analysis in the context of social media content. Data visualization is also a capability that is generating a lot of interest in the corporate world.