The article reviews the principles and fundamentals of gas-assisted focused electron beam (FEB) and focused ion beam (FIB) processing and fabrication. It discusses the properties of electron and ion beams, including their generation, manipulation, and energy distribution. The authors focus on the nonlocal surface effects caused by electron and ion interactions, such as secondary and backscattered electrons, and excited surface atoms. They also explore the mechanisms of electron and ion interaction with molecules, including dissociation, stimulated desorption, polymerization, and sputtering. The article reviews the radial density distribution of surface interactions and the impact of precursor gases on material deposition and removal. It highlights the importance of precursor molecules in FEB and FIB processes and discusses various applications, such as photomask repair, circuit restructuring, and sample sectioning. The review also addresses the challenges and unsolved problems in the field, emphasizing the need for further research to improve the understanding and control of these processes.The article reviews the principles and fundamentals of gas-assisted focused electron beam (FEB) and focused ion beam (FIB) processing and fabrication. It discusses the properties of electron and ion beams, including their generation, manipulation, and energy distribution. The authors focus on the nonlocal surface effects caused by electron and ion interactions, such as secondary and backscattered electrons, and excited surface atoms. They also explore the mechanisms of electron and ion interaction with molecules, including dissociation, stimulated desorption, polymerization, and sputtering. The article reviews the radial density distribution of surface interactions and the impact of precursor gases on material deposition and removal. It highlights the importance of precursor molecules in FEB and FIB processes and discusses various applications, such as photomask repair, circuit restructuring, and sample sectioning. The review also addresses the challenges and unsolved problems in the field, emphasizing the need for further research to improve the understanding and control of these processes.