Starting　with　Dempster＇s　seminal　work,　several　approaches　to　statistical　inference　based　on　belief　functions　have　been　proposed.　Some　of　these　approaches　can　be　seen　as　implementing　some　form　of　prior-free　Bayesian　inference,　while　some　others　put　the　emphasis　on　long-run　frequency　properties　and　are　more　related　to　classical　frequentist　methods.　This　paper　focusses　on　the　latter　class　of　techniques,　which　have　been　developed　independently　and　had　not　been　put　in　perspective　until　now.　Existing　definitions　for　frequency-calibrated　belief　functions　as　well　as　corresponding　construction　methods　are　reviewed,　and　some　new　notions　and　techniques　are　introduced.　The　connections　with　other　frequentist　notions　such　as　confidence　distributions　and　confidence　curves　are　also　explored.　The　different　construction　techniques　are　illustrated　on　simple　inference　problems,　with　a　focus　on　interpretation　and　implementation　issues.　(C)　2017　Elsevier　Inc.　All　rights　reserved.