Like Turing machines, which operate on strings and accept languages, most of the DNA computer models use this linearity as a main force. The information in a DNA molecule is stored in a sequence of nucleotides, also called bases, A,G,C,T (adenine, guanine, cytosine and thymine) joined together by phosphodiester bonds. A single strand of DNA has also a ``beginning'' (usually denoted by 5') and an ``end'' (denoted by 3'). Hence the molecule is oriented. The nucleotides also tend to seek their complements (A is complementary to T and C is complementary to G). This is the well known Watson-Crick complementarity. Two single stranded DNA molecules with complementary sequences of nucleotides and opposite orientation join together through hydrogen bonds and form a double stranded molecule which in space appears as a double helix. When double stranded molecules are heated to 95oC, they disentangle (denature) into single stranded molecules. If single stranded molecules are cooled, they seek their complement and re-anneal into double stranded form. These properties are used by many models of DNA computers. A four letter alphabet can be used $\{A,G,C,T\}$ (in comparison with $\{0,1\}$) and simple operations on the DNA strings can be performed using a few commercially available enzymes that act on the molecules in different ways.
http://www.math.usf.edu/~jonoska/bio-comp/node1.html
Introduction
Papers by Reif on Biomolecular Computing and Self Assembly of DNA Nanostructures (39 papers)
Papers are in PDF format and are in reverse order ( the latest last instead of first )

http://www.cs.duke.edu/~reif/BMC/Reif.BMCproject.html
Biomolecular Computing at Duke
Our recent research mainly deals with the aspect of energy consumption by a computer. We were able to construct a molecular computer whose sole energy source is its input, a combination unthinkable of in the realm of electronic computers. This energy is extracted as the input data molecule is destroyed during computation. As a side-effect we were able to modify our previous molecular computer so that it does not consume software molecules during computation: the only component that changes is the input, while the hardware and the software molecules remain unchanged.
http://www.weizmann.ac.il/mathusers/lbn/
Laboratory for Biological Nanocomputers
The difference with Quantum Computing is dramatic. Quantum Computing involves high physical technology for the isolation of mixed quantum states necessary to implement (if this is scalable) efficient computations solving combinatorially complex problems such as factorization. DNA Computing operates in natural noisy environments, such as a glass of water. It involves an evolvable platform for computation in which the computer construction machinery itself is embedded. Embedded computing is possible without electrical power in microscopic, error prone and real time environments, using mechanisms and technology compatible with our own make up. Because DNA Computing is linked to molecular construction, the computations may eventually also be employed to build three dimensional self-organizing partially electronic or more remotely even quantum computers. Moreover, DNA Computing opens computers to a wealth of applications in intelligent manufacturing systems, complex molecular diagnostics and molecular process control.
http://www.ercim.org/publication/Erc..._caskill1.html
Biomolecular Computing

personally, even though I may not understand all of it, I find this research fascinating...the prospect we may have computers that work on a similiar level to ourselves..the capacity to not only compute but to actually ' think ' is interesting in a matrix sort of way