Search has become an important and necessary component of many diverse ICT applications. A large number of business and application areas depend on the efficiency and availability of search techniques that are capable to process and retrieve heterogeneous and dispersed data. These include: a) the Web, b) mobile devices and applications, c) social networks and social media, and d) enterprise data access and organization. The objective of this document is to provide an overview of the business areas, the research challenges and the socio-economic aspects related to “Search Computing”. The business areas addressed in this paper include, mobile, enterprise, social networks and music, focusing on their current status, their specific technology and application requirements and the new needs arising as a result of these requirements. Specific technologies and challenges are identified such as device limitations and location-based opportunities in mobile search but also challenges that are applicable across domains such as limitations of text-based approaches and new research directions for content-based search. For example, in social networks, new Social Indexing based approaches can incorporate information about the structure and activity of the users’ social network directly into the search and ranking process.