In　the　age　of　artificial　intelligence,　the　best　approach　to　handling　huge　amounts　of　data　is　a　tremendously　motivating　and　hard　problem.　Among　machine　learning　models,　stochastic　gradient　descent　(SGD)　is　not　only　simple　but　also　very　effective.　This　study　provides　a　detailed　analysis　of　contemporary　state-of-the-art　deep　learning　applications,　such　as　natural　language　processing　(NLP),　visual　data　processing,　and　voice　and　audio　processing.　Following　that,　this　study　introduces　several　versions　of　SGD　and　its　variant,　which　are　already　in　the　PyTorch　optimizer,　including　SGD,　Adagrad,　adadelta,　RMSprop,　Adam,　AdamW,　and　so　on.　Finally,　we　propose　theoretical　conditions　under　which　these　methods　are　applicable　and　discover　that　there　is　still　a　gap　between　theoretical　conditions　under　which　the　algorithms　converge　and　practical　applications,　and　how　to　bridge　this　gap　is　a　question　for　the　future.