Communication networks are becoming increasingly important in military operations, with task fields like time-critical targeting, covert special operations, command and control, training, and logistics, all relying heavily on the communication network and its services. On the other hand, commercial communication has dramatically transformed our society and the way we communicate. The newest network mode at present, 5G and beyond (5GB), is characterized by high speed, low latency, high reliability, and high communication density. Although the use of 5GB commercial networks for defense agencies can offer greater flexibility and efficiency, they also face a new challenge that requires high standards of network protection and harsh working conditions and environments. In this paper, we discuss the significance of communication networks in several potential military applications, particularly for warfare, training/drilling, logistics, and special mission-specific stations. We present the communication trends adopted in military applications. Then, we open up various 5GB key performance indexes and their use cases for the military communication systems. We also elaborate on unique challenges of the military communication networks that are unlikely to be resolved via commercial 5GB research. The various 5GB enabling technologies for military communication systems are discussed. Lastly, we present and analyze 5GB new radio for the private military communication under C-band.