Learning　detectors　that　can　recognize　concepts,　such　as　people　actions,　objects,　etc.,　in　video　content　is　an　interesting　but　challenging　problem.　In　this　paper,　we　study　the　problem　of　automatically　learning　detectors　from　the　big　video　data　on　the　web　without　any　additional　manual　annotations.　The　contextual　information　available　on　the　web　provides　noisy　labels　to　the　video　content.　To　leverage　the　noisy　web　labels,　we　propose　a　novel　method　called　WEbly-Labeled　Learning　(WELL).　It　is　established　on　two　theories　called　curriculum　learning　and　self-paced　learning　and　exhibits　useful　properties　that　can　be　theoretically　verified.　We　provide　compelling　insights　on　the　latent　non-convex　robust　loss　that　is　being　minimized　on　the　noisy　data.　In　addition,　we　propose　two　novel　techniques　that　not　only　enable　WELL　to　be　applied　to　big　data　but　also　lead　to　more　accurate　results.　The　efficacy　and　the　scalability　of　WELL　have　been　extensively　demonstrated　on　two　public　benchmarks,　including　the　largest　multimedia　dataset　and　the　largest　manually-labeled　video　set.　Experimental　results　show　that　WELL　significantly　outperforms　the　state-of-the-art　methods.　To　the　best　of　our　knowledge,　WELL　achieves　by　far　the　best　reported　performance　on　these　two　webly-labeled　big　video　datasets.