Metamaterials　with　negative　Poisson＇s　ratio　(NPR)　lattice　structures　have　been　of　considerable　importance　and　interest　in　numerous　engineering　applications.　A　comprehensive　literature　review　on　lattice　structure　design,　mechanical　property,　manufacturing　technique,　and　deformation　mechanism　is　essential　for　developing　novel　metamaterials.　Several　lattice　structure　design　solutions,　including　re-entrant　structures,　chiral　structures,　and　rotating　rigid　structures,　are　presented　in　this　work.　Secondly,　the　associated　mechanical　properties,　including　static　property,　indentation　strength,　and　energy　absorption,　are　discussed.　The　paper　then　presents　some　fundamental　manufacturing　methods　for　lattice　structures　with　NPR,　including　additive　manufacturing,　subtractive　manufacturing,　casting,　snap-fit,　and　welding,　along　with　the　corresponding　deformation　mechanisms.　Finally,　the　conventional　engineering　applications　such　as　medical　and　biomedical　applications,　aerospace　industry,　protective　devices,　strain　sensors,　and　fastener　applications　are　reported,　along　with　a　brief　overview　of　the　potential　applications.　©　2022　Elsevier　Ltd