The　widespread　popularity　of　unmanned　aerial　vehicles　enables　an　immense　amount　of　power　line　inspection　data　to　be　collected.　It　is　an　urgent　issue　to　employ　massive　data　especially　the　visible　images　to　maintain　the　reliability,　safety,　and　sustainability　of　power　transmission.　To　date,　substantial　works　have　been　conducted　on　the　data　analysis　for　power　line　inspection.　With　the　aim　of　providing　a　comprehensive　overview　for　researchers　interested　in　developing　a　deep-learning-based　analysis　system　for　power　line　inspection　data,　this　paper　conducts　a　thorough　review　of　the　current　literature　and　identifies　the　challenges　for　future　study.　Following　the　typical　procedure　of　data　analysis　in　power　line　inspection,　current　works　in　this　area　are　categorized　into　component　detection　and　fault　diagnosis.　For　each　aspect,　the　techniques　and　methodologies　adopted　in　the　literature　are　summarized.　Valuable　information　is　also　included　such　as　data　description　and　method　performance.　In　particular,　an　in-depth　discussion　of　existing　deep-learning-based　analysis　methods　of　power　line　inspection　data　is　proposed.　To　conclude　the　paper,　several　study　trends　for　the　future　in　this　area　are　presented　including　data　quality　problems,　small　object　detection,　embedded　application,　and　evaluation　baseline.