Actually, the transmission was probably one of the main things that persuaded me to get an IS300h. It just seemed such an elegant engineering solution to the problems of the petrol engine.
I've read of conventional automatic gearboxes that have around 370 moving parts. By contrast, I think I've read that the hybrid drive on the first Prius had only 22 moving parts. (Don't quote me but the numbers are something like that.) Having few moving parts seemed like an ideal way to avoid breakdowns, which the Prius reliability record seems to have confirmed.
Here's a random example of what an automatic gearbox looks like when it's taken apart. It's only a three-speed, from a Pontiac TransAm but it shows how many parts there are. Most people won't want to watch more than a minute or two but jump ahead to around 23 minutes in and you can see all the clutch bands. All these parts are potential areas for wear or breakdown.
By contrast, here's a demonstration of the hybrid drive used on Toyotas and Lexuses. A very simple and elegant solution, where the electric motors take the place of the clutch bands in the automatic gearbox. (This lecturer explains things really well but as he talks very slowly I generally increase the youtube playback speed to 1.5 or double speed.)
Here's a graphic display of the hybrid drive power split device. It's been mentioned elsewhere on this forum but it's really useful in helping to understand how the transmission works. Scroll down to the bottom and drag the sliders to control the speed of the gear wheels.