The world is fast moving towards a data-driven society where data is the most valuable asset. Organizations need to perform very diverse analytic tasks using various data processing platforms. In doing so, they face many challenges; chiefly, platform dependence, poor interoperability, and poor performance when using multiple platforms. We present RHEEM, our vision for big data analytics over diverse data processing platforms. RHEEM provides a threelayer data processing and storage abstraction to achieve both platform independence and interoperability across multiple platforms. In this paper, we discuss our vision as well as present multiple research challenges that we need to address to achieve it. As a case in point, we present a data cleaning application built using some of the ideas of RHEEM. We show how it achieves platform independence and the performance benefits of following such an approach.