Networked systems have shown great promises in various cyber-physical applications, such as automotive and transportation systems, smart buildings and infrastructures, and robotic systems. As these systems employ advanced components and interact closely with the dynamic environment, they are often subject to significant disturbances from environment interference, security attacks, and device faults. To ensure system safety, performance and other properties, it is critical to capture these disturbances and reason about their impact at the network level. In this work, we propose to use weakly-hard constraints to specify the disturbances in a bounded manner, and leverage them to formally reason about system properties. We will first present two case studies that demonstrate the impact of disturbances on various properties in networked systems and motivate the usage of weakly-hard constraints. We will then discuss several possible research directions in applying weakly-hard constraints to networked systems.