>>3535964EF-S = lens built for crop sensors like Rebels
EF = cameras built for full frame but will work on crop sensor cameras with a crop factor
You can also adapt on M42/OM/PK and more lenses with an adapter like pic related.
Third parties like Tokina/Tamron/Sigma/Samyang also make lenses that will work on your camera. So long as it says it fits EF mount it'll work.