This chapter discusses the challenges that are imposed by Big Data on the modern and future e-Scientific Data Infrastructure. The chapter discusses a nature and definition of Big Data that include such characteristics as Volume, Velocity, Variety, Value and Veracity. The chapter refers to different scientific communities to define requirements on data management, access control and security. The chapter introduces the Scientific Data Lifecycle Management (SDLM) model that includes all the major stages and reflects specifics in data management in modern e-Science. The chapter proposes the generic SDI architecture model that provides a basis for building interoperable data or project centric SDI using modern technologies and best practices.The chapter discusses how the proposed models SDLM and SDI can be naturally implemented using modern cloud based infrastructure services, analyses security and trust issues in cloud based infrastructure and summaries requirements to access control and access control infrastructure that should allow secure and trusted operation and use of SDI.