Nanotechnology: The field of applied science that deals with assembling matter and developing devices on the 0.1 to 100 nanometer scale.
Biomolecules: Biomolecules are chemical compounds found in living organisms. The most prominent classes of biomolecules are polymeric macromolecules such as amino acid chains (proteins) and nucleic acid chains (DNA and RNA).
Biomolecular Nanotechnology: The field of applied science that explores the use of biomolecules for the assembly and development of nanometer-scale devices. The field has many 'flavors': protein design, DNA & RNA nanotechnology, DNA origami, etc etc.
Proteins and their complexes are unrivaled masterpieces of natural 'biomolecular nanotechnology'. Protein-based molecular machines zig-zag around in the cells of our bodies, restlessly performing atomic-scale life-saving surgical interventions in the midst of a thermal hurricane. These machines have nanometer-scale sizes with atomically precise features. Atomic positional precision is key for their function: protein molecules (and also RNA to some extent) manufacture new molecules, chew-up others, transport cargo, or read what's new on the daily genomic digest. Proteins are built bottom-up by an orchestra of other protein and RNA machines according to instructions stored ultimatively in genomic DNA. If you think of proteins, please think of horn, not of meat.
Many proteins can induce chemical reactions by bringing smaller molecules to precisely specified locations in space and squeezing them a little so that the two educts form a chemical bond (although often already the right spatial orientation is sufficient for a reaction to occur). Some proteins can harness the energy that becomes available when bigger molecules are split into smaller molecules and they use this energy, for example, to actively transport cargo from one place of a cell to another. Other proteins can harness the energy of light or even produce radiation. Proteins interact with each other to create computational circuits. Lest we forget: also isolated RNA and even DNA molecules have been shown to exhibit catalytic and even self-replicating activity (see e.g. the work of Joyce, Szostak, and Breaker). DNA is read, processed, and replicated by protein molecules and serves not only as blueprint for how to construct any given protein but also offers cues when which protein ought to be constructed during the life cycle of a cell.
So, proteins, RNA, DNA and other 'biomolecular-nanotech' parties make cells live, divide, and differentiate into multicellular organisms which then ultimatively make up all the diversity of life that we can still witness on earth and that will hopefully resist the efforts of homo sapiens to extinguish this diversity.
Thus, in short, it seems obvious that a mature technology that makes use of biomolecules has great potential to yield many applications that could broadly improve life on earth. Especially the hetero-polymeric biomolecules such as amino acid chains (proteins), RNA, and DNA have extremely nice features: shape and ultimatively molecular function is encoded in the sequence of monomers that are chained up into polymers. A sensible approach is therefore to learn as much as we can about how Nature plays with these molecules and to timely try to convert the acquired knowledge into a technology. As a side product we will eventually end up with a detailed knowledge of the molecular workings of life.
To move ahead it will be important to solve the following problems:
As already indicated, trying to learn as much as possible from Nature will likely help us in solving these problems. However, learning from Nature is not a small feat, either. We have a serious problem: the documentation of the devices found in Nature is quite poor! The user's manual for how to operate or repair proteins has never been written and their shapes carry evolutionary baggage that conceals the essential design principles. Also, even though one can already sort out the sequence of amino acids that make up a given protein, it is still a hard problem to figure out the shape that it adopts in a cell or how to derive an amino-acid sequence for a designed protein shape that actually does something other than simply aggregating. Lately, there has been exciting progress on the subject of protein structure prediction and design so that we are cautiously optimistic that these problems might be tackled one day. However, for the moment, research on these subjects is a tour-de-force where one-by-one the properties of a given biomolecule have to be experimentally deciphered.
One complication resides in our limited skills in building scientific devices that are commensurate in size to the biomolecule one is interested in. It is hard to study the inner workings of an armwrist watch using pipe tongs. There is a silver lining on the horizon, though. Our understanding of DNA has recently advanced to a level that allows us to start building sophisticated three-dimensional shapes on the nanometer scale using DNA as a construction material. The mission of this lab (current directions / published results) is to develop and apply functional DNA nanostructures that may help to study natural biomolecular systems such as proteins or protein / DNA complexes and to come up with new methods to study these systems, in the hope to accelerate general progress in biomolecular nanotechnology and with the interest to help improving our understanding of the inner workings of life.