Inconsistency arises in many areas in advanced computing. Examples include: Merging information from heterogeneous sources; Negotiation in multi-agent systems; Understanding natural language dialogues; and Commonsense reasoning in robotics. Often inconsistency is unwanted, for example, in the specification for a plan, or in sensor fusion in robotics. But sometimes inconsistency is useful, e.g. when lawyers look for inconsistencies in an opposition case, or in a brainstorming session in research collaboration. Whether inconsistency is unwanted or useful, there is a need to develop tolerance to inconsistency in application technologies such as databases, knowledgebases, and software systems. To address this, inconsistency tolerance is being built on foundational technologies for identifying and analysing inconsistency in information, for representing and reasoning with inconsistent information, for resolving inconsistent information, and for merging inconsistent information. In this introductory chapter, we consider the need and role for inconsistency tolerance, and briefly review some of the foundational technologies for inconsistency tolerance.