As Michael Anissimov notes, the technological singularity as a concept seems to have wormed its way into the public eye to a greater degree than transhumanism as a concept has managed to date. There's probably a lesson or two in there somewhere.
Are we going to see a very steep uptrend in new technologies enabled by biotechnology and computing power? If present exponential trends in the amount of data that can be organized and manipulated continue then we should expect such things as emulated minds, near-complete control over our biochemistry, and molecular manufacturing to exist in the 2040s. The nature of an exponential curve in progress is to produce surprise: growth looks linear for a while, and then all of a sudden an explosion of progress occurs.
We'd all like to lazily find out that we're going to live for a long time in the future thanks to all the hard work being done by other people. For example, there's a contingent who argue that recursively self-improving artificial intelligences will basically allow us to solve all of our information-processing-related problems - the most interesting of which is controlling and repairing age-related damage in our own biology - and that the advent of such AIs within our lifetime is pretty much a given under present trends.
Imagine a future where engineers build a computer with greater-than-human intelligence. This hyper-intelligent being expands its knowledge and brainpower exponentially over days and weeks as it learns how to improve on its own hardware and software design. It starts building 'offspring' even smarter than itself. The sudden arrival of these offspring - cheap, mass-produced super-intelligent machines - sparks explosive economic growth, triggering a series of cascading events.
Nothing in the laws of physics prevents such an outcome, and the production of such artificial intelligences seems inevitable in the long term. But I've long thought that visions of the future allowed by the laws of physics and the nature of present growth curves in biotech and computing inspire a certain complacency in many people. The future will be great, it will bloom from nowhere when the curve takes off, and so no-one has to lift a finger to help now. Our collective fat will be pulled from the fire of aging by the deus ex machina we build.
Or not. For so long as we humans are in the driving seat, I'd argue that you can't compress progress down below a certain pace - the exponential trends will turn linear at some point. We're apparently not at that point yet, given that the trends are all still in place, but I think it's near. If you cut the time taken to produce a good applicable result in science from one year to six months for example, it's still going to take the same amount of time after that point to pull together a company, get funded, sort out the paperwork, and work around the regulations:
I'm dubious about large reductions in the length of business or research cycles through technology while humans are still in the loop. You can certainly make the process cheaper and better, meaning that more attempts at a given business or research model will operate in parallel, but there is a point past which the length of the business cycle cannot be easily compressed. That point is very much a function of the human element: meetings, fundraising, decisions, organizational friction, and so forth - all very time-consuming and proven very resistant to improvements in the time taken. Regulations don't help either - if you want to slow progress, ensure that the end results are not as reliable or effective as they could be, and make the product more expensive, you can't do better than regulation.
My point here is that you shouldn't be dazzled. The future is far from certain, as it is still being built. The trends look very promising, but are by no means a guarantee that the applications of future technology actually built within our lifetimes will include the ones you and I desire. I'm sure we can all rattle off a list of large scale projects that have been possible for decades but never happened - colonizing the oceans, irrigating the Sahara, and so forth. The end of aging and radical life extension in particular will only happen if enough people understand that it can happen, and from that a large enough research and development community is generated to make it happen. Wishful thinking only works when someone, somewhere is getting the job done.