Let's kick off with a bit or revision on the eukaryotic cell, as you are living in several billion of them right now. The text book version looks pretty much like this image I've borrowed from wiki.

There's a membrane (7) enclosing various organelles (9,6), the nucleus (1,2) and several other numbers you can safely ignore for now. And there we have it; life laid bare. Speaking in a generic way, one of these babies is quite capable of living by itself as a single cell organism - yeast for example, or of course making up magnificent beasts such as you and I. But this is all pretty dry stuff and the tubulin I've promised isn't even on Wiki's diagram but looks a bit like number 13 -and forms part of the cytoskeleton.
The cytoskeleton, as its name implies, can be thought of as giving structure to the cell - a kind of fibrous mesh. But it's not a static scaffold, rather it is constantly moving and being rebuilt; responding to changes. How is does this is really remarkable. Textbooks tell us that the cytoskeleton is made up from three types of fiber, microfibres, intermediate filaments and microtubules. I'll even drop the intermediate filaments from the discussion lest it turn into a lecture and just talk about microfibers and microtubules. Don't say I'm not good to you. These 'fibers' are pretty simple, they are composed of repeating units of proteins; actin for microfibers and tubulin for microtubules. A bit like lego:

Image shamelessly borrowed from this paper
Ok I fibbed a bit, there are actually two forms of tubulin (alpha and beta) and in a cell there are plenty of other proteins involved, but you get the idea. Microtubules are directional structures in that one end grows faster than the other and therefore they can move about - quite fast too - by growing. Occasionally, perhaps at the behest of other proteins, they suffer catastrophe and unpeel like a banana. As well as being self-organising, microtubules and the cytoskeleton can respond something that might threaten the cell, a poke with a very small stick for example. This paper shows how the cytoskeleton of a plant cell responds to such a threat - within minutes you have serious rearrangement of microfibers, microtubules and even the endoplasmic reticulum (the pink bit in the wiki cartoon, number 5) gets in the act. Their paper is open source so I hope they don't mind me stitching a couple of their images together for brevity. And open source authors rock - so thanks guys! BTW these are plant cells which are very different to animal cells. Still they are eukaryotes too and I will recklessly carry on...
The real threats are pathogens (fungi, bacteria and oomycetes) which often try to penetrate cells (without consent!) to feed and grow to the detriment of the plant. In this case the cytoskeleton seems to organise the defence to just to spot attacked - and very fast too. How can bundles of proteins 'know' when to realign themselves? I don't have an answer to that question; it's still work in progress. I would love to know. Remember that there's no central organising 'brain' in a cell; LegoMan just can't compete.
Here's another image of eukaryotic cells showing the cytoskeleton (green) with the nucleus (blue) and membrane (red).

As if this wasn't enough, pioneering researchers like Stefan Hell are making nanoscopy feasible. A long-standing dogma had been that light microscopy was fundamentally limited by the wavelength of light. To put that in perspective, tubulin is 8 nm (0.000000008 of a meter) and microtubules 25 nm wide, while the resolution of pretty much all light microscopes until very recently has been an oval of 200 nm by 400-700 nm. This means that if your tagged proteins are closer together than this limit they will look like one blob, not two. Don't get me wrong, confocal (light) microscopy is amazing; it has been simply revolutionary to be able to visualise proteins in living cells. But nanoscopy is jaw-dropping we are now able to visualise single molecules in living cells. There are several techniques being developed (STORM, PALM etc.) but basically they all flip the fluorescent tags on and off on a single molecule basis and thus get around the diffraction limit, achieving resolutions of less than 20 nm by 50-70 nm. I leave you with one last image from a fine open source paper as a taste of things to come. Oh it's actually even better than this, ironically I've ruined the resolution whilst 'borrowing' the image. These are microtubules viewed on the left with confocal microscopy and on the right with nanoscopy. We can now clearly see individual microtubule strands!
I am so excited by these developments because getting around the diffraction limit of light delights the geek in me and there is so much we don't know about how cells and proteins function to create life. We can recognise most of the parts now, but there's no one bit that holds the essence of how that cytoskeleton responds to a poke. It's not a tic-tok mechanism but an emergent property of a complex system filled with precision nanoscale machines. Your cells are infinitely wondrous and now we can see a whole new order of magnitude opening up before us. The next few years will be beautiful.