The　continuous　miniaturization　of　electronic　devices　and　electric　equipment　requires　high　energy-storable　dielectric　capacitors.　Therefore,　seeking　dielectric　materials　with　high　power　density　and　high　energy　density　becomes　more　urgent　for　ensuring　their　reliability.　However,　the　contradiction　between　the　increase　in　the　dielectric　constant　and　breakdown　strength　severely　limits　the　sustainable　increase　in　the　energy　density　of　polymer　dielectrics.　Here,　recent　advances　in　high　dielectric　and　energy　storage　polymer　dielectrics　will　be　introduced.　Polymer　structure　is　an　important　factor　in　determining　dielectric　properties　and　energy　storage　characteristics　of　polymers,　while　the　relationship　between　them　is　still　unclear,　which　hinders　the　design　of　high　energy-storable　polymers.　Our　emphasis　will　be　given　to　how　to　tailor　the　polymer　structures　for　high　dielectric　and　energy-storable　polymer　dielectrics.　The　effect　of　the　polymer　structures　on　the　polarization　and　charge　transport　characteristics　are　also　carefully　discussed　for　further　understanding　the　structure-property　relationship.　Finally,　the　follow-up　research　is　briefly　introduced.　We　intend　that　this　work　will　help　academics　and　industry　toward　high　energy-storable　polymer　capacitors.　©　2021　IEEE.