We're all vaguely familiar with what a kidney looks like, where it resides, and what it does. It's a blob of specialized tissue that sits somewhere in the lower torso and works to filter blood and maintain fluid balance - that sort of thing. It performs a function. But the evolved form of the kidney is far from the only way to achieve this goal, and a kidney is also far removed from the best conceivable ways of performing the its function.
Consider dialysis as a crude example that shows the function of the kidney doesn't have to be performed by a kidney, and nor does it have to be performed in the present location of the kidneys in the body. As this age of biotechnology advances, more and more people are going to purchase and make use of artificial kidneys. At the one end of the scale, you might imagine that kidney 2.0 will be a tissue engineered copy of your failing kidney 1.0 - researchers can almost build them, we know they work, and the only downside is the invasive surgery required to install a new model. But I think we will see a very wide range of kidney 2.0 products that bear as little resemblance to kidney 1.0 as does a dialysis machine.
A pocket calculator does not look like a slide rule, for all it has the same function. Similarly there is no reason to expect the next generation of technology that performs the function of a kidney to resemble either an actual kidney or a present day dialysis machine.
For example, researchers are presently developing bioartificial devices comprised of kidney cells and machinery. It doesn't take too much of a leap of imagination to see that 20 years from now, tiny permeable encapsulations of kidney cells could manufactured by the billion extremely cheaply - and injected once a week to clean the bloodstream from the inside. Alternately, a person might have a dozen implanted bioartificial dialysis machines each the size of a thumbnail sitting beside major arteries. Or kidney function could be incorporated into an implanted artificial heart while the diseased kidneys are removed entirely, and the heart machine itself is a break with the past because doesn't beat, but rather pumps blood continuously.
I've used the kidney as an example, but every organ has it's own set of potential variations, and the present shape and location of each is far from the only way of achieving their different functions. As time moves on, biotechnology developers who think outside the box will hit on new ways of maintaining the functionality of the human body. Many of their results will be very different to the organs we're equipped with today, and some will be far superior.