Most greybox fuzzing tools are coverage-guided as code coverage is strongly correlated with bug coverage. However, since most covered codes may not contain bugs, blindly extending code coverage is less efficient, especially for corner cases. Unlike coverage-guided greybox fuzzers who extend code coverage in an undirected manner, a directed greybox fuzzer spends most of its time allocation on reaching specific targets (e.g., the bug-prone zone) without wasting resources stressing unrelated parts. Thus, directed greybox fuzzing (DGF) is particularly suitable for scenarios such as patch testing, bug reproduction, and specialist bug hunting. This paper studies DGF from a broader view, which takes into account not only the location-directed type that targets specific code parts, but also the behaviour-directed type that aims to expose abnormal program behaviours. Herein, the first in-depth study of DGF is made based on the investigation of 32 state-of-the-art fuzzers (78% were published after 2019) that are closely related to DGF. A thorough assessment of the collected tools is conducted so as to systemise recent progress in this field. Finally, it summarises the challenges and provides perspectives for future research.