This paper introduces responsive systems: systems that are real-time, event-based, or time-dependent. There are a number of trends that are accelerating the adoption of responsive systems: timeliness requirements for business information systems are becoming more prevalent, embedded systems are increasingly integrated into soft real-time command-and-control systems, improved message-oriented middleware is facilitating growth in event-processing applications, and advances in service-oriented and component-based techniques are lowering the costs of developing and deploying responsive applications. The use of responsive systems is illustrated here in two application areas: the defense industry and online gaming. The papers in this special issue of the IBM Systems Journal are then introduced. The paper concludes with a discussion of the key remaining challenges in this area and ideas for further work.