Untethered　microgrippers　that　can　navigate　in　hard-to-reach　and　unpredictable　environments　are　significantly　important　for　biomedical　applications　such　as　targeted　drug　delivery,　micromanipulation,　minimally　invasive　surgery　and　in　vivo　biopsy.　Compared　with　the　traditional　tethered　microgrippers,　the　wireless　microgrippers,　due　to　the　exceptional　characteristics　such　as　miniaturized　size,　untethered　actuation,　dexterous　and　autonomous　motion,　are　projected　to　be　promising　microtools　in　various　future　applications.　In　this　review,　we　categorize　the　untethered　microgrippers　into　five　major　classes,　i.e.　microgrippers　responsive　to　thermal,　microgrippers　actuated　by　magnetic　fields,　microgrippers　responsive　to　chemicals,　light-driven　microgrippers　and　hybrid　actuated　microgrippers.　Firstly,　the　actuation　mechanisms　of　these　microgrippers　are　introduced.　The　challenges　faced　by　these　microgrippers　are　also　covered　in　this　part.　With　that,　the　fabrication　methods　of　these　microgrippers　are　summarized.　Subsequently,　the　applications　of　microgrippers　are　presented.　Additionally,　we　conduct　a　comparison　among　different　actuation　mechanisms　to　explore　the　advantages　and　potential　challenges　of　various　types　of　microgrippers.　In　the　end　of　this　review,　conclusions　and　outlook　of　the　development　and　potential　applications　of　the　microgrippers　are　discussed.　©　2019,　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.