Quantum simulation with neutral atoms has enabled engineering and probing quantum matter in new parameter regimes and with compelling novel probes. Individual snapshots can reveal the position and spin of each atom in the system thereby providing access to complex correlations in materials that are often crucial to understand their behaviour. In my talk, I will discuss recent progress on quantum simulation with ultracold bosonic and fermionic atoms and molecules in optical lattices and tweezers. The physics of strongly correlated electronic materials can e.g. be efficiently realized using ultracold fermionic atoms. Tuneable lattice geometries allow one to introduce programmable geometries and mixed dimensional situations in which doping can continuously tuned. I will show, how pairing of charge carriers and extended stripe-like structures emerge under such conditions due to an interplay of mobile dopant, mixed dimensions, and an antiferromagnetic background. Quantum simulation also offers new possibilites for probing out-of-equilibrium dynamics. I will present recent results on the observation of Hilbert space fragmentation in two-dimensionsl. Preparing localized defects on top of states within such fragments has also enables us to observe fractonic excitations. Their dynamics is shown to play a fundamental role when connecting thermalizing and non-thermalizing states of different fragments connected through a domain wall boundary.
Finally, I will show how polar molecules provide an alternative platform for realizing long-range interacting itinerant systems but have for a long time been plagued by uncontrolled losses. I will delineate how such losses can be overcome using microwave radiation and gives rise to novel field-linked scattering resonances that allow assembling larger ultracold molecular complexes also opening the route to p-wave superfluids.