Manipulating the ground state of a quantum mechanical system reveals valuable information about the state itself as well as the associated quantum critical behavior. Here, we discuss two experimental realizations of model spin Hamiltonians and show how the ground states can be varied by external tuning mechanisms. SrCu2(BO3)2 is one of the few real-world materials that corresponds to the Shastry-Sutherland model, with corner-sharing Cu S=1/2 dimers lying on a square lattice. We have mapped out the development from isolated dimers to long-range magnetic order via a high-pressure, high-resolution x-ray synchrotron study using a diamond anvil cell cooled down to cryogenic temperatures. We are able to track explicitly the suppression of the singlet-triplet gap at a second-order quantum phase transition, followed at higher pressure (~4.5 GPa) by a first-order structural/magnetic transition. The Transverse-Field Ising Model, with its interplay between spin interactions and quantum tunneling, provides a rich laboratory for studying aspects of basic quantum mechanics. I will focus on the dipole-coupled Ising crystal, LiHoxY1-xF4. For x=4.5%, we show that the equilibrium state of the system depends on the thermodynamic boundary conditions between the crystal and an external heat reservoir, permitting controllable switching between states dominated by thermal vs. quantum fluctuations. A similar selectivity can be achieved by following specific cooling trajectories while using a transverse magnetic field to tune the rate of quantum tunneling in the material.