Recently, we have been witnessing huge advancements in the scale of data we routinely generate and collect in pretty much everything we do, as well as our ability to exploit modern technologies to process, analyze and understand this data. The intersection of these trends is what is called, nowadays, as Big Data Science. Cloud computing represents a practical and cost-effective solution for supporting Big Data storage, processing and for sophisticated analytics applications. We analyze in details the building blocks of the software stack for supporting big data science as a commodity service for data scientists. We provide various insights about the latest ongoing developments and open challenges in this domain. Big Data Systems Meet Machine Learning Challenges: Towards Big Data Science as a Service