Data acquisition and data recovery are essential to any e-discovery or digital forensic process. However, these two aspects seem to be considerably difficult in a cloud-computing environment. The very nature of the Cloud raises a number of technical and organizational challenges, which renders traditional approaches and tools inapplicable. Resource pooling, rapid elasticity, and geographical distribution of data are only a small part of the Cloud’s features that hinder the forensic investigation. At the same time, there is significant absence of forensic readiness in cloud computing policy framework. In this chapter, the authors discuss the challenges pertaining to data acquisition in a cloud environment and discuss possible directions for meeting these challenges by presenting representative cases and sketching acquisition process and scenarios.