Recent years have witnessed a tremendous development of vertical gallium nitride (GaN) power devices, a new class of device technology that could be the key enabler for next-generation high performance power electronics. In this comprehensive review, we discuss the recent progress made on vertical GaN power devices, highlighting their important device design principles and fabrication processes. Part I of the two-part review series introduces the basic design principles of vertical GaN devices using Schottky barrier diodes (SBDs) and p-n diodes as examples. We provide a comprehensive review and in-depth analysis on their basic structures, fabrication processes, and device physics. Materials engineering, including buffer layer and drift layer design, and device engineering, including various edge termination methods, are elucidated. Key device topics, including avalanche breakdown and leakage mechanisms of vertical GaN power devices, are also discussed. We also examine various approaches and provide detailed descriptions of the key knowledge obtained. This timely review provides valuable information for the power electronics community and can inspire researchers for future interdisciplinary collaborations in this emerging and exciting research field.