W.R. Dykes in 1913 and Rodionenko in 1961 were among those making major contributions to classification. The following classification, by G.H.M. Lawrence, with modifications based on the work of Brian Mathew, is provisional pending further study. (Common names and comments are mine. Two- and three-letter codes are abbreviations commonly used for the group.)
I. Subgenus Iris (the bearded irises) A. Section Iris (the eupogons, or pogons) 1. Subsection Miniature Dwarf Bearded (MDB) <8" 2. Subsection Standard Dwarf Bearded (SDB) 8-15" 3. Subsection Intermediate Bearded (IB) 16-27" 4. Subsection Miniature Tall Bearded (MTB) 16-27" 5. Subsection Border Bearded (BB) 16-27" 6. Subsection Tall Bearded (TB) >27" B. Section Psammiris C. Section Oncocyclus D. Section Regelia E. Section Hexapogon F. Section Pseudoregelia II. Subgenus Limniris (the beardless irises) A. Section Lophiris (the evansia, or crested irises) B. Section Limniris a. Series Sibiricae (SIB) (1) Subseries Sibiricae (2) Subseries Chrysographes b. Series Tenuifoliae c. Series Californicae (the Pacific Coasts, PCI) d. Series Syriacae e. Series Chinensis f. Series Ruthenicae g. Series Unguiculares h. Series Spuriae (SPU) i. Series Foetidissimae (the "Roast Beef" iris) j. Series Laevigatae (incl. Versicolors, Virginica, JI, Pseudacorus) k. Series Prismaticae l. Series Hexagonae (the Louisianas, LI) m. Series Ensatae (Lactea) n. Series Longipetalae (the Rocky Mountain iris) o. Series Tripetalae (including setosa) p. Series Vernae III. Subgenus Nepalensis IV. Subgenus Xiphium (Dutch, Spanish, English) V. Subgenus Scorpiris (the Junos) VI. Subgenus Hermodactyloides (the reticulatas)
In general, the subgenuses can be distinguished by underground parts: Subgenus Iris with rhizomes, Nepalensis from daylily-like fleshy rhizomes, Xiphium from bulbs, and Scorpiris from bulbs with fleshy roots. Within Subgenus Iris, Section Iris (the bearded irises) can be distinguished from Section Limniris (the beardless irises), by the presence of caterpillar-like structures crawling out onto the lower petals. More complete distinguishing characteristics and species names and more can be found in the excellent general references.
The Iris, by Brian Mathew, Batsford, 1989, 256 pages, 38 colour photos, 32 b/w photos, 16 illustrations, ISBN 0-7134-6039-3, is a serious guide to the genus, with descriptions, classifications, and habitat information.
A Guide to Species Irises: Their Identification and Cultivation does a good job at its aim. The Species Group of the British Iris Society edited this book to 371 pages, published by Cambridge University Press, 1997. ISBN 0-521-44074-2
A Guide to Bearded Irises: Cultivating the Rainbow for Beginners and Enthusiasts by Kelly D. Norris, Timber Press, 2012, is the newest book on the subject and has excellent reviews. 352 pages, 318 color photos, ISBN-10: 1604692081, ISBN-13: 9781604692082. Kindle edition available.
Another one is IRIS, by Fritz Köhlein, Timber Press, 1987, 370 pages, 210 color photos, 48 line drawings, ISBN 0-88192-049-5. From a more European perspective, he discusses and pictures some species and varieties that are less commonly grown in the USA, research less rigorous than others here. about $35
The Louisiana Iris, edited by Marie Caillet and Joseph K. Mertzweiller, pub. by the Society for Louisiana Irises, 1988, 233 pages, 93 color photos, 23 b/w photos, 16 illus., ISBN 0-914641-09-3. This is a beautiful and well-done book on the topic, maybe the best of the iris specialty books. about $23
The Japanese Iris, edited by Currier McEwen for The Society for Japanese Irises, 1990. This is an excellent and beautiful reference book covering the subject. about $29
The Siberian Iris, edited by Currier McEwen for The Society for Siberian Irises, published by Timber Press in 1996, ISBN 0-88192-329-x has 242 pages, 37 color photos, covers the subject comprehensively. about $40.
Most can be obtained through the American Iris Society, which also publishes a series of checklists, updated from time to time. These are a reference to the many registered varieties. Timber Press can be reached at 800-327-5680.