Antibody Reformatting

An antibody isn't just an antibody. There's a lot a protein engineer can do with an antibody!
When we talk about antibodies we're typically referring to a human or mouse monoclonal antibody, which is comprised of 2 heavy chains and 2 light chains for a total of 12 immunoglobulin domains and an approximate molecular weight of 150kD. Antibodies are able to bind antigens via the combined binding surface created by a variable heavy (VH) and a variable light (VL) immunoglobulin domain. An antibody has two VH/VL pairs and thus is divalent and can bind two copies of the same antigen.
We aren't limited to this antibody configuration when we build therapeutic proteins. Protein engineers use a technique called antibody reformatting to design proteins of various sizes and multiplicity of antigen binding sites, even enabling binding of two or more different antigens. 
A Fab has one antigen binding site (monovalent) and is produced by removing an 'arm' from a full antibody. It's composed of the VH and CH1 of a heavy chain and the VL and VC of a light chain, and has a molecular weight of about 50kD. 
The smallest antibody-derived format is called an scFv, or single-chain variable fragment, and it comes in at roughly 28kD. An scFv is built by joining together the VH and VL domains into a single polypeptide chain via a flexible linker sequence. This format typically shows poorer yields in production but offers increased design flexibility especially in the context of a larger therapeutic molecule.
Diabodies are created by further engineering of an scFv's linker sequence. Shorter linker sequences can lead to dimerization of VH and VL with the VL and VH, respectively, of a neighboring chain. So for only ~60kD you can build a divalent molecule!
Every part an antibody has utility. The Fc region, which is composed of the CH2 and CH3 domains of each heavy chain, can be fused to a variety of non-immunoglobulin proteins to create Fc-fusion proteins. Addition of the Fc can extend the half-life of these 'other' proteins and expand the diversity of the therapeutic space.
A related, though unique, reformatting component for the protein engineer is the VHH, also known as a nanobody or sdAb. A VHH is a single immunoglobulin domain capable of interacting with an antigen. It's not derived from the human or mouse antibodies discussed here, but is instead a product of the camelid immune response. VHH tend to be quite stable and, at 15kD, are efficient building blocks in therapeutic protein design.