Composite　materials/structures　are　advancing　in　product　efficiency,　cost-effectiveness　and　the　development　of　superior　specific　properties.　There　are　increasing　demands　in　their　applications　to　load-carrying　structures　in　aerospace,　wind　turbines,　transportation,　medical　equipment　and　so　on.　Thus,　robust　and　reliable　non-destructive　testing　of　composites　is　essential　to　reduce　safety　concerns　and　maintenance　costs.　There　have　been　various　non-destructive　testing　methods　built　upon　different　principles　for　quality　assurance　during　the　whole　lifecycle　of　a　composite　product.　This　article　reviews　the　most　established　non-destructive　testing　techniques　for　detection　and　evaluation　of　defects/damage　evolution　in　composites.　These　include　acoustic　emission,　ultrasonic　testing,　infrared　thermography,　terahertz　testing,　shearography,　digital　image　correlation,　as　well　as　X-ray　and　neutron　imaging.　For　each　non-destructive　testing　technique,　we　cover　a　brief　historical　background,　principles,　standard　practices,　equipment　and　facilities　used　for　composite　research.　We　also　compare　and　discuss　their　benefits　and　limitations　and　further　summarise　their　capabilities　and　applications　to　composite　structures.　Each　non-destructive　testing　technique　has　its　own　potential　and　rarely　achieves　a　full-scale　diagnosis　of　structural　integrity.　Future　development　of　non-destructive　testing　techniques　for　composites　will　be　directed　towards　intelligent　and　automated　inspection　systems　with　high　accuracy　and　efficient　data　processing　capabilities.　©　The　Author(s)　2020.