Recent advances in nanofabrication techniques allow to confront effective theories of strongly correlated electrons in low dimensions with experiment. I will review recent experiments on quantum dots and quantum wires. A major problem of fundamental importance is to describe strongly correlated electrons out of thermal equilibrium, which is typical in quantum dot experiments. We discovered that exact and universal results about one of the basic quantum dot configurations can be obtained out of equilibrium using an effective conformal field theory. I will present the corresponding predictions for experiment, which show intriguing behavior associated with quantum criticality and multiple electron scattering. It will be emphasized that finding the correct effective field theory plays a central role in the whole area of many body physics, and as an additional example, interacting spin 1/2 fermions in one dimension, which posses universal singularities near their excitation threshold, will be discussed.