As mentioned on the page ‘What Makes Hawaiʻi Unique’ an excellent introduction to the general concepts of evolution in Hawaiʻi is the primer Evolution in Hawaiʻi, A Supplement to Teaching About Evolution and the Nature of Science developed by the National Academy of Sciences and is available here: http://nap.edu/10865 and the clickable table of contents is here: https://www.nap.edu/read/10865/chapter/1#v.
For a quick introduction this article is very good: http://www.bbc.com/earth/story/20150625-islands-where-evolution-ran-riot.
An excellent website on evolutionary radiation with example from Hawaiʻi from the Cornell lab is here: https://www.allaboutbirds.org/news/why-evolution-goes-wild-on-islands-the-science-of-adaptive-radiation/.
An interesting study that was conducted by Price and Clague (2002) including fruitflies, damselflies, various species of birds, and plants is How old is the Hawaiian biota? Geology and phylogeny suggest recent divergence (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1691179/pdf/12495485.pdf). Several groups are evaluated. An updated analysis for the flora is discussed below.
EXAMPLES
The Honeycreepers
These birds are the most well-known example of Hawaiian evolution to most of the public. The bird shown above is an Iiwi (image credit: Mauiforestbirds.org). Other examples are shown below.



A study Multilocus Resolution of Phylogeny and Timescale in the Extant Adaptive Radiation of Hawaiian Honeycreepers available at: https://doi.org/10.1016/j.cub.2011.09.039 illustrates the importance of the islands geologic history in the evolution of Hawaiian birds. Another finding from this study was that the ancestor of Eurasian rosefinches is the closest relative to all the extant Hawaiian honeycreepers. An excellent multi-media illustration in the paper is Figure 2 titled Bayesian Divergence Date Estimates for Hawaiian Honeycreepers from Whole Mitochondrial Genomes Based on Three Island Age Calibration Points.
A nice summary of this article is here: https://www.theguardian.com/science/punctuated-equilibrium/2011/nov/02/Hawaiian-honeycreepers-tangled-evolutionary-tree.
Invertebrates
Other groups of Hawaiian fauna, especially invertebrates, also are amazing examples of evolution in the Hawaiian islands, such as the Hawaiian tree snail shown above (image credit: Hawaii DLNR) and including many other groups as shown in the photos below. See other pages on this website for their stories.

Plants
Plants are another exceptional example of Hawaiian evolution. The photo above is from the Puu Kukui Watershed Preserve (photo credit: National Park Service). Many of these endemic species are now endangered and the Plant Extinction Prevention Program (PEPP) is working hard to save them. More information is in the Flora pages of this website.

A lecture slide series from a botany class Biogeography of Hawaiʻi taught by Ken Systsma at UW-Madison had a slide series illustrating how plant species dispersed to Hawaiʻi based on available information (A= wind, B=wings, and D=waves). Unfortunately, a website that was open to the public in 2019 now seems to be available only through the school course.
Some of the information may have been obtained from the Price and Wagner (2018) paper Origins of the Hawaiian flora: Phylogenies and biogeography reveal patterns of long‐distance dispersal: https://onlinelibrary.wiley.com/doi/10.1111/jse.12465 which is available for free in complete form. Appendix 1 of the paper provides a list of each colonist along with its origin (presumed), primary dispersal mode, and best literature citation.
A summary of the origins of the Hawaiian flora from the paper is shown in the table below.
Region | Total # lineages | Total # endemic species | Total # native species |
Australasian | 28 | 77 | 84 |
Indo‐Malayan | 31 | 215 | 219 |
East Asian | 10 | 174 | 175 |
Neotropical | 34 | 116 | 127 |
North American | 30 | 195 | 201 |
Widespread | 78 | 43 | 110 |
Unknown | 48 | 120 | 123 |
Total | 259 | 940 | 1039 |
They also tallied the frequencies of different dispersal modes from best available information which were as follows: flotation – 50, external bird – 90, internal bird – 72. External bird dispersal was most prevalent when the origin was North America, and internal bird dispersal was most prevalent when the origin was the Pacific region and Australasia.
A short video explaining dispersion by wings, water, and wind is here: https://video.nationalgeographic.com/video/news/0000014e-44d2-dd38-ab4e-ffd754920000.
Price and Clague (2002) list age estimates (most recent common ancestor) for many groups of Hawaiian organisms that range from 0.5 (Metrosideros spp.) to 26 million years ago (Hawaiian fruitflies): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1691179/pdf/12495485.pdf.
An example of the origin of the Hawaiian species of Viola in which the original species was likely transported by birds, as depicted in the presentation in the K. Systsma course is below.

The Hawaiian lobelioids in the bellflower (Campanulaceae) plant family are an amazing example of adaptive radiation in plants. The below figure is from the K. Systsma course. They represent the largest plant radiation in Hawaiʻi and with a great diversity in habitat, growth form, pollination biology, and seed dispersal. Note however that the figure considers the group to be evolved from 3-5 colonizers – a more recent assessment based on genetics indicates only ONE COLONIZER (see more information on the Lobelias page of this website).

Another example are the Hawaiian silverswords. The below figure is also from the K. Systsma course.

Additional discussion of the origins of the Hawaiian endemic flora is in Chapter 4 of the book The Biology of Island Floras describes research on the origins of Hawaiian endemics based on molecular studies in ‘Origin and evolution of Hawaiian endemics: new patterns revealed by molecular phylogenetic studies’ by S. Keeley and V. Funk (2011): https://repository.si.edu/bitstream/handle/10088/17450/bot_Keeley_Funk_color_Bramwell.pdf.
Various patterns of Hawaiian evolutionary histories for several groups of insects, Tetragnatha spiders, and honeycreepers are discussed in a chapter of the book Hawaiian Biogeography: Evolution on a Hot Spot Archipelago in an article byW. L. Wagner and V. A. Funk available here: https://www.researchgate.net/publication/284062056_Biogeographic_patterns_in_the_Hawaiian_Islands. Updates to some of that work based on molecular studies is in a paper titled ‘Molecular biogeography and diversification of the endemic terrestrial fauna of the Hawaiian Islands’ by Cowie and Holland (2008) and is here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607369/
Another interesting study: The true tempo of evolutionary radiation and decline revealed on the Hawaiian archipelago https://www.nature.com/articles/nature21675 (abstract, full article not free). They used a “geologically informed model” to “infer the rates of species richness change for 14 endemic groups over their entire evolutionary histories”. They summarize “We find that these endemic clades underwent evolutionary radiations characterized by initially increasing rates of species accumulation, followed by slow-downs. In fact, for most groups on most islands, their time of evolutionary expansion has long past, and they are now undergoing previously unrecognized long-term evolutionary decline.”