The song's titular character, a powerful man who talks to "his world" and to himself by telephone, abuses both the women (whom he "owns") and the men (sending them "pebbles and stones") in his charge. The lyrics deal with feminism, the emotional distance and cruelty sometimes shown by men, and the dehumanizing of both sexes.
Pitchfork Media's Jess Harvell stated, "On Orange Factory's 'Down and Dirty' remix of 'Yang Yang', Ono is vocodered into a Troutman-esque gremlin and blurred into an anonymous orgasmic sigh over a brutally functional garage bounce." Dan Rapper, in his review of Open Your Box for PopMatters, opined that the Orange Factory remix "is turned into a straight vocoder-style Ministry of Sound track, its squelching electro already somehow tired-sounding."
"Yang Yang" was covered by Anika and released as the lead single from her debut album Anika in September 2010. The song was offered as the "Free MP3 of the Day" on Spinner. On her choice to cover the song for her album, Anika explained, "I loved the way the words sounded and as an ex-politics student and political journalist, I thought the song would make a great cover. Yoko Ono is renowned for her political views but I think there was a dark side to the lyrics that the original version had not fully explored."
Heather Phares from Allmusic described the song as a "fantastic anti-pop single, with klaxon-like synths providing the hook and a bassline so strutting it could have been stolen from a blaxploitation soundtrack." John Doran, in his review for NME, commented, "Just when you thought the post-punk genre had been strip-mined for all potential inspiration, along comes Anika."
Drowned in Sound included Anika's cover of "Yang Yang" on its list Singles of the Year 2010.