Modelling　the　failure　process　of　a　repairable　system　is　vitally　important　in　many　industrial　sectors　such　as　the　offshore　industry　and　the　transport　industry,　in　which　properly　maintaining　assets　is　needed.　Among　the　various　models,　the　geometric　process　(GP)　has　been　widely　applied,　mainly　in　the　reliability　and　maintenance　engineering,　since　its　introduction.　A　book　on　the　GP　was　published　in　2007　and　included　the　GP-related　research　by　that　year.　However,　since　then,　much　research　has　been　conducted,　which　creates　a　necessity　to　review　the　existing　publications　relating　to　the　GP,　its　various　extensions　and　applications　since　2007.　This　paper　serves　for　this　purpose.