Where the earlier taxonomy systems have been based on the look of the plant or its sex organs, like Carl Linnaeus suggested in 1753, or other characteristics, the new science open up for a more accurate image of the relationship between the plants through DNA. This is the Angiosperm Phylogeny Group's third approach, the first can be seen on: APG while this second s found on APGII.

APG III was published on the 8. of October 2009. It is made up by the former 45 orders with additional 14 new: Amborellales, Nymphaeales, Chloranthales, Petrosaviales, Trochodendrales, Buxales, Vitales, Zygophyllales, Picramniales, Huerteales, Berberidopsidales, Escalloniales, Bruniales and Paracryphiales.
Here are no more "bracketed families", and the number of families have gone down from 457 to 415. Of these, some are new: Petermanniaceae, Schoepfiaceae, Limeaceae, Lophiocarpaceae, Montiaceae, Talinaceae, Anacampserotaceae, Centroplacaceae, Calophyllaceae, Guamatelaceae, Gerrardinaceae, Dipentodontaceae, Capparidaceae, Cleomaceae, Cytinaceae, Mitrastemonaceae, Metteniusaceae, Linderniaceae, Thomandersiaceae and Quintiniaceae.
The not sorted families are reduced to 10 from 39. It still have some unanswered questions, which might be solved in APG IV?

More systems and the history behind.