Lattice Monte Carlo approaches to the many-body problem generally involve two kinds of (controlled) uncertainties: statistical and systematic. Dealing with the latter implies performing calculations for a variety of parameter values (volumes, lattice spacings, masses, etc.) followed by an extrapolation to the desired limit (continuum, thermodynamic, etc.). As we shall see, recent advances in the design of improved actions and operators, based on the ideas of renormalization, provide an efficient way to approach the continuum limit of lattice calculations, from non-relativistic systems to QCD. Statistical uncertainties, on the other hand, are typically addressed in a more straightforward manner: by obtaining more samples. For many observables and problems of interest, nevertheless, statistical noise can get in the way of research in a dramatic (in fact, exponential) way. Still, one may ask the question: can we learn anything about the problem by listening to the noise?