The influence is generally narrowed down to Tommorow Never Knows and perhaps their studio work in Sgt Peppers
The primacy of dancible groove and sound design/production over melody (even if it does have a decent hook). My opinion towards Tomorrow Never Knows has soured from my original perception that it is a ground breaking masterpiece because I think it is a bad influence on music as a whole.
In terms of core elements such as songwriting. Song structure (ie they predominantly write in a verse/bridge structure rather than verse/chorus and usage of multi-part), chord progression and the elevation of vocal melodies to its peak in popular music
Considering we are living in a era of music where people believe there is a “death of melodies” as a primary mode of expression they are almost not influential at all to music in the here and now
Alice cooper said it the best “Cooper stated that in his opinion the cause of the problem was that certain modern bands "had forgotten to listen to the Beatles".