I will review recent progress of the optical lattice emulators of the Fermi Hubbardmodel. The new feature of these experiments is availability of snapshots of many-body states with single particle resolution. I will discuss new insight from theseexperiments on the properties of magnetic polarons in antiferromagnetic Mottinsulators. I will also discuss the idea of using quantum simulators to performinference of NMR spectra for biological molecules. Practical aspects of realizingthis hybrid quantum-classical algorithm on currently available experimentalplatforms will be reviewed.