This article explores teleoperation for remote presence applications from a human-robot interaction (HRI) perspective to create a model that captures the key elements of the system and projects the impact of ever-increasing advances in autonomy and communications connectivity. Remote presence applications are those where one or more humans use the robot to project themselves into an environment to complete a time-critical mission. In these applications, there is some compelling need to have human perception at a distance. For example, the environment may be unsafe or unreachable, such as encountered when searching for survivors in the aftermath of a disaster, or the situation is novel and perceptually unconstrained, as in noticing a hidden terrorist during a hostage situation. Remote presence applications are characterized by "the observers won't know what needs to be seen until they see it" flavor and the need to see that critical "what needs to be seen" in as near real time as possible. This means that remote presence applications are inherently teleoperated; the human is an active element in the control loop, and there is no benefit to full autonomy. The question becomes how to transfer the advances in autonomy and communications to enable the human-robot enterprise to successfully and reliably complete its mission.