One of the drawbacks of Flash video so far was that iPhone and iPad couldn't play it. SkyFire, an application on top of Safari lets you view Flash video on iPhone and iPad.
How it exactly works can be found in the video below created by the folks of SkyFire themselves:
More on the subject can be found in this article: Skyfire Brings Flash Video To The iPad (And Sells Out)
However, Skyfire has its problems. Several customers complained about erratic behavior, so it is clear that solutions like this are not perfect.
How about HTML5 support?
A lot happened in recent months. Slowly, HTML5 is picking up and thanks to the efforts of Longtailvideo, some features typically for Flash are being supported now. HTML5 compatible skins do no longer prevent media from playing on Apple iOS devices. Playlists and post images are possible now. Streaming is still a problem, but this might change in the future.
Here is the current state of affairs: The State of HTML5 Video Report. It is update regularly, so you might want to bookmark the article.