Wireless multihop ad hoc networks are vulnerable to several specific security threats. In particular, a number of papers exist in the literature where sinkhole, blackhole, grayhole and selfish attacks are studied for this kind of networks. All of these malicious behaviors can be grouped into a general class known as packet dropping attacks and constitute a serious risk for communications, services and users. This paper provides a complete overview on the abovementioned packet discarding related security threats for multihop ad hoc networks, the most known security approaches being organized and discussed according to the defense line they are intended to cover: prevention, detection or response. Additionally, to clarify the efforts and proposals made until now by the community, open challenges and new trends in this field are also pointed out. In summary, the present paper constitutes a relevant contribution for interested researchers to better understand packet dropping related defenses in wireless multihop ad hoc networks.