©　Springer　International　Publishing　AG　2017.As　a　significant　role　in　industrial　equipment,　rotating　machinery　fault　diagnosis　(RMFD)　always　draws　lots　of　attention　for　guaranteeing　product　quality　and　improving　economic　benefit.　But　non-stationary　vibration　signal　with　a　large　amount　of　noise　on　abnormal　condition　of　weak　fault　or　compound　fault　in　many　cases　would　lead　to　this　task　challenging.　As　one　of　the　most　powerful　non-stationary　signal　processing　techniques,　wavelet　transform　(WT)　has　been　extensively　studied　and　widely　applied　in　RMFD.　Many　previous　publications　admit　that　WT　can　be　realized　by　means　of　inner　product　principle　of　signal　and　wavelet　base.　This　paper　verifies　the　essence　on　inner　product　operation　of　WT　by　simulation　experiments.　Then　the　newer　development　of　WT　based　on　inner　product　is　introduced.　The　construction　and　applications　of　major　developments　on　adaptive　multiwavelet　in　RMFD　are　presented.　Finally,　super　wavelet　transform　as　an　important　prospect　of　WT　based　on　inner　product　are　presented　and　discussed.