In this article, a cognitive management framework is proposed for ensuring exploitation of the Future Internet of Things (FIoT). Cognitive systems offer self-x and learning. A cognitive system has the ability to dynamically select its behavior through self-management/awareness functionality, taking into account information and knowledge on the context of the operations as well as policies and including the generation of the context itself. The framework is based on the principle that any real world object and any digital object that is available, accessible, observable or controllable can have a virtual representation in the Future Internet, which is called Virtual Object (VO). Basic VOs can be composed in a more sophisticated way by forming Composite VOs (CVOs), which provide services to high-level applications and end-users. The described paradigm is applied to various applications scenarios: smart home, smart office, smart city and smart business. This paper presents some background in IoT, identifies the requirements and challenges, and sets the directions that should be followed.