Our children will be growing up into a tumultuous world of big changes, the forced moving-on from oil and the changes that's going to bring to geopolitics, the real rise of India and China to positions of economic and, perhaps, social dominance. The fading thrashings of the US as it is finally forced to admit it's no longer the world power it once was (I don't see them doing this with the relative grace of the British Empire) greater European integration and, hopefully, a revolution of democratic politics as the corporate domination of the socio-political structure reaches a point where it becomes unacceptable and obvious even to the common man.
Technology will continue to liberate and enslave in equal measure but the real problems are going to be energy and aging populations. Our children are likely to have to work hard for little reward and we're unlikely to be left much to give them. They'll have to support us, either directly or indirectly and this may create pressure to have larger families again, something the planet can ill afford.
It's hard to predict even five years into the future these days, given the pace of change, but I have a feel the environmental and energy crises will create a hiccough in Moore's Law and arrest development for a while. That and certain physical limitations and usefulness limitations. Do we need all this massive computing power in our pockets if we're not doing specialist applications? Not really...
It'll be changeable, turbulent, but it'll be a meaningful period, perhaps more so than our lifetimes.