Big Data visualization relies on an interdisciplinary research area that includes mass data storage and retrieval, operations, analytics, security, ethics as well as visualization and interaction with end users. This paper reports on the characteristics of Big Data systems, mainly focusing on information visualization and discusses a number of methods towards this direction, analyzing research issues and challenges that emerge. Additionally, this paper discusses new approaches for Big Data visualization in the context of Ambient Intelligence (AmI) environments, highlighting new aspects in the field in respect to information presentation and natural user interaction. Furthermore, a scenario of Big Data visualization in AmI environments is presented, aiming at bringing to surface the new potential of such approaches in terms of interaction simplification, and adaptation to the context of use.