Wireless communication has achieved great success in the past several decades. The challenge is of improving bandwidth with limited spectrum and power consumption, which however has gradually become a bottleneck with evolution going on. The intrinsic problem is that communication is modeled as a message transportation from sender to receiver and pursues for an exact message replication in Shannon's information theory, which certainly leads to large bandwidth and power requirements with data explosion. However, the goal for communication among intelligent agents, entities with intelligence including humans, is to understand the meaning or semantics underlying data, not an accurate recovery of the transmitted messages. The separate first transmission and then understanding is a waste on bandwidth. In this article, we deploy semantics to solve the spectrum and power bottleneck and propose a first understanding and then transmission framework with high semantic fidelity. We first give a brief introduction of semantics covering the definition and properties to show the insights and scope of this paper. Then the proposed communication towards semantic fidelity framework is introduced, which takes the above mentioned properties into account to further improve efficiency. Specially, a semantic transformation is introduced to transform the input into semantic symbols. Different from the conventional transformations in signal processing area, for example discrete cosine transform, the transformation is with data loss, which is also the reason that the proposed framework can achieve large bandwidth saving with high semantic fidelity. Besides, we also discuss semantic noise and performance measurement. To evaluate the effectiveness, a case study of audio transmission is carried out. Finally, we discuss the typical applications and open challenges.