Asparagaceae is a family that in the past has been considered to contain only a few genera of perennials usually with tuberous roots, what looks like leaves that are needle like and white starry flowers with 6 tepals and stamens and a 3 chambered ovary. The fruit is a red or black berry. The principal genus in this narrowed view is Asparagus.
APG II in 2003 proposed expanding this family optionally to include other families, many of which were once included in Liliaceae. Under this proposed system this family consists of monocots with flowers arranged in racemes with the exception of Themidaceae which has umbels, but plants in this family have many bracts where the other broad group Alliaceae has umbels and only two bracts. Below are the families optionally included. This becomes more complicated because some of these families were expanded by some taxonomists in 2000 to include other families. If we have made a wiki family page (shown in blue) some of the possibilities are listed. Earlier books still are using the previous family names and not everyone is embracing APG II.
Anemarrhenaceae -- included optionally by APG II in Agavaceae if not included in Asparagaceae
Behniaceae -- included optionally by APG II in Agavaceae if not included in Asparagaceae
Herreriaceae -- included optionally by APG II in Agavaceae if not included in Asparagaceae