Beardless Iris most commonly grown are
Louisiana Iris
These come from the Mississippi River area of the USA. They are evergreen and one of the few irises that like tropical areas, although they will grow in most of Australia. They like moist acid soil and flower in October- November.
Spuria Iris
Spuria Iris come from central Europe. They usually go dormant for a while in autumn. They grow in a wide range of soils (especially alkaline) but need a cool winter and dislike extreme summer humidity. Flowering is in October-November
Siberian Iris
These come from Europe. They need a frosty winter to flower well, flowering time is usually November. The best situation is a damp sunny spot and they are dormant in autumn to early winter.
Japanese Iris
These are often called iris kampherii after one of the original species that the modern hybrids were bred from. Flowering in November - December they like damp, acid soil with cold winters and will be dormant for autumn-winter.
Pacific Coast Iris
Coming from the west coast of the USA, these are low growing, extremely drought hardy irises that need a sunny spot with acid soil. They must only be moved in late autumn to early winter.
and a wide range of other hybrids and species