zero. The ultracold atoms play the same role as the electrons; they are kept at very low densities in order not to form an ordinary solid, and the extreme cooling allows them to behave as quantum-mechanical particles. A standing wave of laser light—that is, an evenly spaced series of maxima and minima of light intensity—traps the atoms in a perfectly periodic artificial crystal (optical lattice), free from any defect or impurity (see the figure). Unlike electrons, atoms are electrically neutral, but they can interact when they get very close and collide one with each other. A first spectacular demonstration of the possibility of using cold atoms to make quantum simulation of condensed-matter models (4) was the direct observation of the quantum phase transition from a superfluid BoseEinstein condensate to a strongly correlated Mott insulator (5) of bosons, particles with integer spin that can multiply occupy a single quantum state. Anderson localization of matter waves was also demonstrated very recently in cold bosonic gases either with laser speckles (6) or with disordered optical lattices (7). More insight into the physics of conduction can be obtained by using atoms that are fermions. Manipulation of ultracold fermions started with the first production of a degenerate Fermi gas of K atoms (8) and has now become a rich and fast-developing field (9, 10). Fermionic atoms have been trapped in optical lattices (11), and the transition from a conductive state to a band-insulating state for noninteracting (noncolliding) fermions was observed by studying their transport properties through the optical lattice (12). Very recently, a Mott insulating state for ultracold interacting fermions was reported (13). Schneider et al. make an important step forward in the experimental investigation of the fermionic Hubbard model, the fundamental model describing interacting spin-1/2 fermions in a periodic potential. The fermionic gas can be switched from a metal to a band insulator to a Mott insulator “on demand,” depending on the ratio of the relevant energy scales set in the system. A decisive advance of this work is the independent control of the number of particles, the strength of interactions between them, the mobility of the particles across the lattice, and the size of the system, the latter being controlled by the application of an external trapping potential. In particular, the collisions between the neutral atoms (mimicking the electric repulsion between the electrons) are controlled by applying an external magnetic field across a Fano-Feshbach resonance (14), which allows tuning of the interaction strength between atoms. Schneider et al. also present direct measurement of the compressibility of the ultracold gas, that is, its ability to change size after a variation of the trapping potential. This capability allowed them to fully characterize the different insulating phases. The experimental results are in excellent agreement with the predictions of a dynamic mean-field treatment of the Hubbard model (15). Quantum simulation with cold atoms is becoming a mature field of research. Experimental possibilities of control and detection have reached a level high enough to allow validity checks of different theoretical approaches. The experimental investigation of spin mixtures of fermions in optical lattices has just started, and new exciting adventures are waiting, such as the use of cold atoms as quantum simulators of high-temperature superconductors, the investigation of quantum magnetism, and the study of interacting fermions in the presence of disorder (16). There is also the possibility of using atoms of different chemical species to create ultracold dipolar molecules or to study exotic kinds of superfluid pairings.