As “low altitude economy” is included in the government reports， it become the hot topic in 2024. Due to the advantages of high efficiency， flexibility， low cost， and multi payload， unmanned aerial vehicles （UAVs） are regarded as the main form of “low altitude economy”. As the key factor to guarantee flight safety and communication security， the spectrum management of UAV communication is an indispensable factor in promoting the vigorous development of the “low altitude economy”. This paper starts with the changes of UAV spectrum management policies from 2015 to 2023， and then deeply explores the regulations， standards and technologies of UAV communication， including the operating frequency bands and flight supervision， as well as standard specifications represented by international organizations， such as International Telecommunication Union （ITU）， Institute of Electrical and Electronics Engineers （IEEE） and The 3rd Generation Partnership Project （3GPP）. The subjects of channel models and interference mitigation strategies that closely related to UAV communication spectrum management are also discussed. Finally， current challenges and future research directions of UAV communication spectrum management are presented.