Communication stands as a potent mechanism to harmonize the behaviors of multiple agents. However, existing work primarily concentrates on broadcast communication, which not only lacks practicality, but also leads to information redundancy. This surplus, one-fits-all information could adversely impact the communication efficiency. Furthermore, existing works often resort to basic mechanisms to integrate observed and received information, impairing the learning process. To tackle these difficulties, we propose Targeted and Trusted Multi-Agent Communication (T2MAC), a straightforward yet effective method that enables agents to learn selective engagement and evidence-driven integration. With T2MAC, agents have the capability to craft individualized messages, pinpoint ideal communication windows, and engage with reliable partners, thereby refining communication efficiency. Following the reception of messages, the agents integrate information observed and received from different sources at an evidence level. This process enables agents to collectively use evidence garnered from multiple perspectives, fostering trusted and cooperative behaviors. We evaluate our method on a diverse set of cooperative multi-agent tasks, with varying difficulties, involving different scales and ranging from Hallway, MPE to SMAC. The experiments indicate that the proposed model not only surpasses the state-of-the-art methods in terms of cooperative performance and communication efficiency, but also exhibits impressive generalization.