This thesis focuses on collective behavior in low-dimensional quantum many-body systems that are closely related to experimental settings. We start by describing the evolution of a localized electron spin in a semiconductor quantum dot. The focus is on the influence of direct interactions with the nuclear spins in the underlying substrate, and on the role of a changing configuration of the nuclear spins, mediated by dipole interactions. We then continue with a description of a scanning tunneling microscope experiment, in which cobalt atoms are manipulated to form linear chains. By comparing the experimental data with a theoretical model, we show that the cobalt chains can be described by the spin-1⁄2 XXZ Heisenberg model in a transverse field, and that the experiment demonstrates signatures of the finite size onset of quantum criticality for increasing chain length. Next, we consider the case of infinitely repulsive bosons, brought out of equilibrium by an instantaneous Bragg pulse. We study the difference between evolution in a homogeneous background and in a harmonic trapping potential, and observe that the effects associated to the harmonic trapping potential only set in after pre-relaxation due to hard-core interactions. We also discuss the efficiency of momentum transfer through finite duration Bragg pulses, and conclude that protocols designed for free bosons perform significantly less well for strongly interacting bosons. Finally, we extend to finite but strong interaction effects through a self-consistent mean-field description. We observe that the dynamics of observables is slowed down as a consequence of a decreased sound velocity.