Understanding the collective behavior of many-particle systems is a major intellectual challenge in modern physics. Even when the interactions between particles are well understood, as is the case in condensed matter, the correlated motion of large numbers of particles leads to emergent phenomena that require new experimental probes and new modes of thinking. Our experimental research explores systems of reduced dimensionality at low temperatures and high magnetic fields where collective effects can lead to new phases of matter and to dramatic changes in behavior. We employ scanning tunneling microscopy, spectroscopy and transport techniques to probe these properties and harness them for device applications.