This thesis introduces a novel framework for enabling intelligent machines and robots with the fifth-generation (5G) cellular network technology. Autonomous robots, such as Unmanned Aerial Vehicles (UAVs), Autonomous Guided Vehicles (AGVs), and more, can notably benefit from multi-agent collaboration, human supervision, or operation guidance, as well as from external computational units such as cloud edge servers, in all of which a framework to utilize reliable communication infrastructure is needed. Autonomous robots are often employed to alleviate humans by operating demanding missions such as inspection and data collection in harsh environments or time-critical operations in industrial environments - to name a few. For delivering data to other robots to maximize the effectiveness of the considered mission, for executing complex algorithms by offloading them into the edge cloud, or for including a human operator/supervisor into the loop, the 5G network and its advanced Quality of Service (QoS) features can be employed to facilitate the establishment of such a framework. This work focuses on establishing a baseline for integrating various time-critical robotics platforms and applications with a 5G network. These applications include offloading computationally intensive Model Predictive Control (MPC) algorithms for trajectory tracking of UAVs into the edge cloud, adapting data sharing in multi-robot systems based on network conditions, and enhancing network-aware surrounding autonomy components. We have identified a set of key performance indicators (KPIs) crucially affecting the performance of network-dependent robots and applications. We have proposed novel solutions and mechanisms to meet these requirements, which aim to combine traditional robotics techniques to enhance mission reliability with the exploitation of 5G features such as the QoS framework. Ultimately, our goal was to develop solutions that adhere to the essential paradigm of co-designing robotics with networks. We thoroughly evaluated all presented research using real-life platforms and 5G networks.