Apparently, electrons themselves have never actually been observed?

Well, that's not strictly true. "Observation" does not mean "visibly seen" - we can detect and measure electron charge, for example, among other properties, thus "observing" the electron itself. To be able to "see" an electron with our eyes in the way you (presumably) mean would just be to capture electromagnetic radiation of a certain frequency generated by/reflected from the electron. That's pretty arbitrary when you think of all the different ways electrons (and other particles) can interact with things in a detectable manner, allowing us to observe them and their effects.
Also, they have managed to capture film of an electron's motion, which I don't think is quite the same as filming the electron itself in the way we'd think of it, but is still pretty damn cool. Press Release; pop-science article; scientific paper. I won't try to explain the physics behind how they did that unless somebody particularly wants me to.