Will this lens work with my camera?

I'm not talking about any specific lens, or even camera for that matter, but I didn't know how to condense what I wanted to ask into a simple question…
I'm just wondering if it's assumed that all lenses compatible with your DSLR also have the ability to be compatible with auto-focus. For example, I have a Canon T3i right now (I'm either switching to the Nikon d5100 or the T4i as soon as possible), which is able to obviously auto-focus while shooting photos. Will there be lenses that aren't compatible with that feature, and don't auto-focus even when the camera is set to?
I'm actually mostly concerned about continuous auto-focus in video mode. When I have the d5100 or the T4i, I want to know if it's assumed all lenses compatible with those cameras are also compatible to continuously auto-focus when I'm shooting video.
Hopefully I wasn't too confusing?

Nikkor lenses are all compatible with Nikon dSLR cameras. All AF-S lenses are compatible with all Nikon dSLR cameras. Entry level dSLR cameras can only auto-focus using AF-S lenses, but must be manually focused if you use legacy Nikkor AF lenses.
All Canon EF lenses are compatible with all Canon dSLR cameras, but you Can't use EF-S lenses on any of the Canon full frame cameras (5D and 1D series bodies).
You will have to ask the dealer which of the Nikon or Canon cameras can auto-focus in the video mode.

Any of the Canon EOS lenses should be able to autofocus with the Canon T3i and T4i. Some lenses are supposed to be better than others in working with the claimed improvement in live-view focusing of the Canon T4i. Canon claims their new EF 40mm STM and EF-S 18-135mm STM (not the same as the older non-STM 18-135mm) will have faster autofocus with the T4i, although other lenses can still work.
Nikon AF-S lenses can autofocus with the D5100. There are non-AF-S lenses that would be manual focus only with that camera. So far there's no announcement of an improved live-view system for the Nikon F mount cameras.
The Nikon 1 system, which uses its own special lenses claims to have a kind of extra fast phase and contrast detect live view autofocusing--the kind of thing Canon is using in the T4i.
The Canon EOS, Nikon F, and Nikon 1 systems are not cross-compatible.

Only Nikon has issues with autofocus on some lenses with some bodies to cut cost on their cheapest dSLR models. With the right lens, those cheapest Nikon dSLR's will autofocus without problems. Canon also has issues with lens compatibility especially with newer bodies and older lenses (but they don't admit it). Sony bodies also work with the older Minolta autofocus lenses. Pentax will work with any lens made for it and that includes the old screwmount lenses (that will need a cheap adapter of course).
Not all dSLR's autofocus continuously during video. In fact very few (one?) do. If you're main concern is video, get a video camera. The extent of controls a video camera has far outweighs the benefits of a dSLR and the lens it provides.

If you buy the T4i, then all the lenses you currently have for your T3i… Will be fully compatible. However, when using the T4i's Continuous AF during movie recording, all sounds the lens makes will also be recorded.
Canon has released two new STM (linear stepper motor) lenses that have been optimized for using with the new T4i and offer smooth and silent Continuous AF during movie recording, so no lens sounds will be recorded.
Read about them here…
http://www.usa.canon.com/...5_6_is_stm
http://www.usa.canon.com/..._f_2_8_stm
http://www.dpreview.com/...rebel-t4i/
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