Year-on-year, advancing technology automates processes that once required human effort. This puts people out of work in one sense, but in another sense it frees up that same human effort for other things, which are often - though certainly not always - more pleasant or creative. Thus, while a generation or two ago I would almost certainly have been plugging away as a clerk in a monstrous Kafkaesque insurance firm, today I get to do fun research. Wait, I hear you say, there were scientists two generations ago, surely? Yes, but very few, and as a consequence, the only full-time ones were probably vastly more talented than I am, and probably luckier too.
In general, it's the things machines are bad at that become the work of tomorrow. Who would have thought, in 1950, say, that there'd be as many hairdressers as there are today? Hairdressing requires the kinds of motor skills and creativity that is hard to automate, and lots of people enjoy getting what were once movie-star-only treatments. Hence the trend.
But not all creative professions grow. Ones in which the product can be replicated by technological means can actually shrink. A classic example is musicians: once upon a time you had to hire one in order to even hear a tune, now you can put on a CD and listen to Herbie Hancock or Itzhak Perlman or whoever, which has increasingly put medicore players out of business.
So the formula is this: jobs which are both hard to automate and can't be easily replicated tend to be the ones that grow. With that in mind, what occupations might swell their ranks in the years ahead? Research (of course!), and I think especially applied and translational work, which there could be so, so much more of. But also less obvious things like personal services - cooking, surgery, hairdressing etc. Maybe personal shoppers: technology is making shopping for clothes harder, inasmuch as there more choice, so I think there might be a growing demand for experts who do it all for you. Professional childcare should rise: surely everyone wants a Super Nanny on call? Teaching should keep growing, at least until classroom sizes grow small enough that no one cares about further reductions, and demographic changes mean there aren't actually many kids to teach.
So close your eyes and wonder: what would you like to have done for you, if it were really cheap? Whatever it is, odds on your grandchildren will be doing it, having it done for them, or, if you're a really demanding dreamer, still be wishing for the same thing.