Device to Device (D2D) communication was first considered in out-band to manage energy issues in the wireless sensor networks. The primary target was to secure information about system topology for successive communication. Now the D2D communication has been legitimated in in-band by the 3rd Generation Partnership Project (3GPP). To initiate D2D communication, Device Discovery (DD) is a primary task and every D2D application benefits from DD as an end to end link maintenance and data relay when the direct path is obstructed. The DD is facing new difficulties because of the mobility of the devices over static systems, and the mobility makes it more challenging for D2D communication. For in-band D2D, DD in a single cell and multi-cell, and dense area is not legitimated properly, causing latency, inaccuracy, and energy consumption. Among extensive studies on limiting energy consumption and latency, DD is one of the essential parts concentrating on access and communication. In this paper, a comprehensive survey on DD challenges, for example single cell/multi-cell and dense area DD, energy consumption during discovery, discovery delay, and discovery security, etc., has been presented to accomplish an effective paradigm of D2D networks. In order to undertake the device (user) needs, an architecture has been projected, which promises to overwhelm the various implementation challenges of DD. The paper mainly focuses on DD taxonomy and classification with an emphasis on discovery procedures and algorithms, a summary of advances and issues, and ways for potential enhancements. For ensuring a secure DD and D2D, auspicious research directions have been proposed, based on taxonomy.