ThestudyofthecontrolandstabilizationoftheKdVequationbeganwiththeworkofRussellandZhanginlate1980s.Bothexactcontrolandstabilizationproblemshavebeenintensivelystudiedsincethenandsignificantprogresseshavebeenmadeduetomanypeople'shardworkandcontributions.Inthisarticle,theauthorsintendtogiveanoverallreviewoftheresultsobtainedsofarinthestudybutwithanemphasisonitsrecentprogresses.Alistofopenproblemsisalsoprovidedforfurtherinvestigation.