The electromagnetic fields of point sources with time varying charges moving in the vacuum are derived using the Liénard-Wiechert potentials. The properties of the propagation velocities and the Doppler effect are discussed based on their far fields. The results show that the velocity of the electromagnetic waves and the velocity of the sources cannot be added like vectors; the velocity of electromagnetic waves of moving sources are anisotropic in the vacuum; the transverse Doppler shift is intrinsically included in the fields of the moving sources and is not a pure relativity effect caused by time dilation. Since the fields are rigorous solutions of the Maxwell’s equations, the findings can help us to abort the long-standing misinterpretations concerning about the classic mechanics and the classic electromagnetic theory. Although it may violate the theory of the special relativity, we show mathematically that, when the sources move faster than the light in the vacuum, the electromagnetic barriers and the electromagnetic shock waves can be clearly predicted using the exact solutions. Since they cannot be detected by observers in the region outside their shock wave zones, an intuitive and reasonable hypothesis can be made that the superluminal sources may be considered as a kind of electromagnetic blackholes.