"Xenobots" are an advancement in the world of micro and nanobots within the medical field. They are the first macro-organism, if you're willing to call them that, which reproduces through kinematic self-replication.
The concept of kinematic self-replication had previously been observed with macromolecules only, never a structure of this size. The principle relies on the motion or otherwise mechanical behavior of the parent to form a viable child via the rearrangement of molecules/cells within the environment.
This is distinct from the behavior of "nano-spiders", which are molecular beings on the nano-scale which are programmed to walk along DNA. They are made from a mixture of streptavidin and half-stranded DNA.
The main difference between Xenobots and nano-spiders is the scale at which they operate and the ability for Xenobots to not only exhibit emergent behavior, but also replicate. The medical and scientific applications of both are incredibly promising, but the ability to replicate makes the Xenobots all the more powerful... and all the more scary.
Top: Generated Xenobot shapes.
Bottom: Artistic depiction of nano-spiders.
Top: Xenobot generation and fitness example.
Bottom: Simulation vs. reality comparison for Xenobots.
The Xenobot is a clump of around 3000 embryonic cells taken from Xenopus laevis, a frog, hence the name. When these cells begin in the embryonic stage of life, while they would normally later develop into perhaps skin or organ cells, they have the plasticity in their genetics to develop emergent behavior. By forming a clump of these cells, the cells plastically embark on a new path instead of their natural programming.
The shape of the Xenobot is dictated by the researcher (Sam Kriegman, Douglas Blackiston, Michael Levin, and Josh Bongard; scientists are UVM, Tufts, and Harvard) and is designed through the use of a genetic algorithm which simulates the Xenobot and selects for the intended behavior — in this case, reproduction. The shape which the algorithm converged upon is a Pac-Man-like form which gathers cells within the environment, compresses them in the "mouth" and then eventually results in an almost exact copy of the original Xenobot. The optimal shape ensures the longest number of successive generations before the lineage terminates. For other tasks that Xenobots are known to accomplish such as swimming, walking, transferring of materials, etc, different shapes are more suitable.
So to answer the question "who makes a Xenobot?" Well, researchers, artificial intelligence, and most importantly Xenobots.