With the depletion of conventional oil reservoirs and concerns about the increasing carbon footprint of coal, natural gas is poised to play a much bigger role in sustainable economic growth. Gas hydrates being an abundant source of clean methane have created great interest among academia and industry. Its demographic occurrence in shallow depths has motivated industry and academia to explore its abundance and exploitation potential. Despite being shallow, offshore gas hydrate exploration and drilling is a deepwater endeavor, which was considered expensive and risky as a result of its narrow thermodynamic stability and lack of exploitation experience. However, with recent advancement in technology and long-term field trials, it has been universally accepted that methane production from marine hydrate reservoirs is achievable with innovative drilling techniques and proper well design pertaining to the appropriate location and layout of wells, efficient well orientation, competent casing and tubing design, and completion design requirements for long operating life and reliability of the well. Much has been discussed about exploration and production, but very little has been addressed about the drilling technologies that have the potential for safe and effective exploitation of this resource in commercial quantities. The objective of this review is to enlighten the readers with exploration techniques used to locate gas hydrate reservoirs and discuss drilling tools and techniques that have the potential to avoid premature hydrate dissociation around the wellbore and enhance production life of the well with minimum interventions. The techniques discussed are mostly the learnings from the international drilling projects on different types of gas hydrate reservoirs. This review also focuses on different drilling fluids, pressurized coring systems, and well logs suitable for hydrate reservoirs. We believe that this review will provide a scientific reference material to engineers for safe exploration and drilling and stimulate upcoming exploration and drilling activities in the field of gas hydrates.