[4] It was Deep Purple's last album by the Mark II line-up with singer Ian Gillan and bassist Roger Glover until 1984’s Perfect Strangers.

[5] Although its production and the band's behaviour after its release showed the group in turmoil, with frontman Gillan remarking that "we'd all had major illnesses" and felt considerable fatigue, the album was a commercial success.

"[6] Ian Gillan left the band following this album, citing internal tensions – widely thought to include a feud with guitarist Ritchie Blackmore.

However, in an interview supporting the Mark II Purple comeback album Perfect Strangers, Gillan stated that fatigue and management had a lot to do with it: We had just come off 18 months of touring, and we'd all had major illnesses at one time or another.

One of them is from magazine Melody Maker of July 1972, where drummer Ian Paice remarks: Deep Purple get piles of passionate letters either violently against or pro the group.

In the United States, it sold half a million copies in its first three months, achieving a gold record award faster than any Deep Purple album released up to that time.

"[12] In a retrospective critical review, Eduardo Rivadavia of AllMusic expresses the same opinion and writes that, apart from "Woman from Tokyo", the album's songs are "wildly inconsistent and find the band simply going through the motions", although he does praise "Rat Bat Blue".

[5] On the contrary, reviewer David Bowling writes in the Blogcritics site that Who Do We Think We Are "is one of the band’s strongest and stands near the top of the Deep Purple catalogue in terms of quality", providing "some of the best hard rock of the era".