Encountered-Type Haptic Displays (ETHDs) provide haptic feedback by positioning a tangible surface for the user to encounter. This permits users to freely eliciting haptic feedback with a surface during a virtual simulation. ETHDs differ from most of current haptic devices which rely on an actuator always in contact with the user. This article intends to describe and analyze the different research efforts carried out in this field. In addition, this article analyzes ETHD literature concerning definitions, history, hardware, haptic perception processes involved, interactions and applications. The paper proposes a formal definition of ETHDs, a taxonomy for classifying hardware types, and an analysis of haptic feedback used in literature. Taken together the overview of this survey intends to encourage future work in the ETHD field.