Eudicots - Clade
Flowering plants (Angiospermae alt Magnoliophyta) are known to have existed since more than 160 million years ago. Some branches, such as Nymphaeales (water lilys) and Magnoliids are from very early times and are called Basal Angiosperms. The Monocots (grasses, palms, etc.) appeared some time before 110 million years ago and are also sometimes called basal angiosperms. The Eudicots (means "true dicots") appeared around 110 million years ago. They now account for more than 70% of all flowering plants.
More on Magnoliophyta / Angiosperms.
Our classifications follow the APG III system (Angiosperm Phylogeny Group). Applying molecular analysis, the AGP system has caused a major upheaval in plant taxonomy. The APG divides this clade into "Basal Eudicots" and "Core Eudicots" but this technicality is irrelevant to culinary activities. Eudicots are such a large and confusing clade, even the APG folks are having a hard time organizing them, so some groups are labeled "clade", which means their rank is still uncertain. Some families aren't assigned to an Order yet, and some Orders aren't yet assigned to a Clade. With phylogeny in flux, different references may put the same plant in different families. Basically, the more certain we become of specific pieces, the more confusing the whole puzzle becomes.
Basal Eudicots - Clade
Core Eudicots - Clade
Asterids - Clade
Core Eudicots - Non Astrid