Fiber　structures　with　nanoscale　diameters　offer　many　fascinating　features,　such　as　excellent　mechanical　properties　and　high　specific　surface　areas,　making　them　attractive　for　many　applications.　Among　a　variety　of　technologies　for　preparing　nanofibers,　electrospinning　is　rapidly　evolving　into　a　simple　process,　which　is　capable　of　forming　diverse　morphologies　due　to　its　flexibility,　functionality,　and　simplicity.　In　such　review,　more　emphasis　is　put　on　the　construction　of　polymer　nanofiber　structures　and　their　potential　applications.　Other　issues　of　electrospinning　device,　mechanism,　and　prospects,　are　also　discussed.　Specifically,　by　carefully　regulating　the　operating　condition,　modifying　needle　device,　optimizing　properties　of　the　polymer　solutions,　some　unique　structures　of　core–shell,　side-by-side,　multilayer,　hollow　interior,　and　high　porosity　can　be　obtained.　Taken　together,　these　well-organized　polymer　nanofibers　can　be　of　great　interest　in　biomedicine,　nutrition,　bioengineering,　pharmaceutics,　and　healthcare　applications.　©　2019　by　the　authors.