A molecular computer  is a single molecule which transforms into a predictable another one, by a cascade of random chemical reactions mediated by a collection of enzymes, without any external control.
We could use the artificial chemistry chemlambda to build real molecular computers. There is a github repository  where this model is implemented and various demos are available.
By using molecular bricks which can play the role of the basic elements of chemlambda we can study the behaviour of real molecules which suffer hundreds or thousands of random chemical reactions, but without having to model them on supercomputers.
A molecule designed like this will respect for a while the chemlambda predictions… We don’t know for how much, but there might be a window of opportunity which would allow a huge leap in synthetic biology. Imagine instead of simple computations with a dozen of boolean gates, the possibility to chemically compute with recursive but not primitive recursive functions.
More interesting, we might search for chemlambda molecules which do whatever we want them to do. We can build arbitrarily complex molecules, called chemlambda quines, which have all the characteristics of living organisms.
We may dream bigger. Chemlambda can unite the virtual and the real worlds… Imagine a chemical lab which takes as input a virtual chemlambda molecule and outputs the real world version, much like Craig Venter’s printers. The converse is a sensor, which takes a real chemical molecule, compatible with chemlambda and translates it into a virtual chemlambda molecule.
Applications are huge, some of them beneficial and others really scary.
For example, you may extend your immune system in order to protect your virtual identity with your own, unique antibodies.
As for using a sensor to make a copy of yourself, at the molecular level, this is out of reach in the recent future, because the real living organism works by computations at a scale which dwarfs the human technical possibilities.
The converse is possible though. What about having a living computer, of the size of a cup, which performs at the level of the whole collection of computers available now on Earth?