In the last few years, considerable attention has been given to in vitro models in an attempt to reduce the use of animals and to decrease the rate of preclinical failure associated with the development of new drugs. Simple two-dimensional cultures grown in a dish are now frequently replaced by organotypic cultures with three-dimensional (3-D) architecture, which enables interactions between cells, promoting their differentiation and increasing their in vivo likeness. Microengineering now enables the incorporation of small devices into 3-D culture models to reproduce the complex microenvironment of the modeled organ, often referred to as organs-on-a-chip (OoCs). This review describes various OoCs developed to mimic liver, brain, kidney, and lung tissues. Current challenges encountered in attempts to recreate the in vivo environment are described, as well as some examples of OoCs. Finally, attention is given to the ongoing evolution of OoCs with the aim of solving one of the major limitations in that they can only represent a single organ. Multi-organ-on-a-chip (MOC) systems mimic organ interactions observed in the human body and aim to provide the features of compound uptake, metabolism, and excretion, while simultaneously allowing for insights into biological effects. MOCs might therefore represent a new paradigm in drug development, providing a better understanding of dose responses and mechanisms of toxicity, enabling the detection of drug resistance and supporting the evaluation of pharmacokinetic–pharmacodynamics parameters.