This paper is the first part of a two-part paper that documents a detailed survey of the research carried out on consistency and latency in distributed interactive applications (DIAs) in recent decades. Part I reviews the terminology associated with DIAs and offers definitions for consistency and latency. Related issues such as jitter and fidelity are also discussed. Furthermore, the various consistency maintenance mechanisms that researchers have used to improve consistency and reduce latency effects are considered. These mechanisms are grouped into one of three categories, namely time management, information management, and system architectural management. This paper presents the techniques associated with the time management category. Examples of such mechanisms include time warp, lock step synchronization, and predictive time management. The remaining two categories are presented in part II of the survey.