This is a selection of Olivia's official compilation albums. It is difficult to track down all the releases as they frequently vary from country to country. I've listed the ones that seemed to be done with Olivia's support (and promotion) first, then some of the better compilations done by her former record companies, with the rest bringing up the rear.
Only the first four collections really have a place in a collection unless you're an ONJ completist. Many recent compilations are compilations of Olivia's early work prior to 1974/5 after which it seems control passed from the record companies to ONJ productions. Most of these are from when Olivia was in the UK, they may be unfamiliar to her wider US audience but US fans will know them well. As a result her earlier folk-themed songs are excessively represented on collections, even modern CD ones. It's nice to hear these tracks , but now that we can create our own playlists we don't need them sliced and diced so many ways.
The notable exception is the 1992 Back To Basics album, which was promoted by Olivia at the time. The Greatest Hits 1,2 are probably the best compiled selections along with the "Back To Basics" CD which was to launch her 1992 comeback is an excellent selection, with four new tracks on it. Fate did not smile on Olivia and her comeback tour which was canceled when she was diagnosed with breast cancer (which was successfully treated).
Some of the these later compilations have a remarkable similarity between the tracks and even running order. In a world which is moving towards mp3 players holding one's entire collection and sale of individual tracks it's hard to see the raison d'etre for so many CD compilations featuring such a small subset of her work.
These next albums helped many fans in the late 1970s to early Nineties complete their collections of the early tracks
In those pre-internet days tracking down albums that were no longer widely carried or were deleted was very difficult compared to now.
Various compilations from over the years