The age of Big Data has begun, and our computing needs and technology are at a crossroads. Cloud computing has become the dominant computing model for processing Big Data in recent years. The flexibility and cost savings made possible through migration to a cloud have encouraged many companies to use clouds for their critical applications. Unfortunately, today’s clouds have major security issues related to the confidentiality, integrity, availability, and privacy of the data and applications outsourced to the cloud. Multi-tenancy and other inherent properties of the cloud computing model have introduced novel attack surfaces and threats. Clouds and their clients are also the target of new types of attacks that threaten their trustworthiness, reliability, and economic sustainability. Unless these issues are resolved, clouds cannot and should not be used for sensitive Big Data applications such as defense-related data and intelligence, financial transactions, or medical records.