"Transhumanism" is already here, in a way. We have medications including some complex drugs, most people at least take multi-vitamins, we have surgeries and sometimes do weird stuff like transplant limbs or faces. Even simpler, we have knowledge of diet and health which lets us stay in better shape than before (though a lot of people are in worse shape due to junk food...we have access to high-protein diets and effective exercises though).
On the other hand, "transhumanism" where we upload our consciousness or modify ourselves to the point where we don't resemble humans anymore, probably won't come for a long time. Even problems like aging and disease and significantly hard to solve. Most of what we know about the human brain is psychology and large-scale things like hormones. Because evolution is a process which doesn't favor simplicity or straightforwardness, and the brain and body have trillions of microscopic cells all working more or less simultaneously - we don't have nearly enough computational power or resources or technology to even remotely "thoroughly" understand this.
I think in the near future we will gradually develop more bionic and cybernetic augmentations, like improving on those bionic arms and legs I heard about a few years ago, and implanted chips and medications. But it's going to be gradual and take a long time, and some things are just nearly impossible.