Extracellular vesicles (EVs) have emerged as a potential therapy for several diseases. These plasma membrane-derived fragments are released constitutively by virtually all cell types—including mesenchymal stromal cells (MSCs)—under stimulation or following cell-to-cell interaction, which leads to activation or inhibition of distinct signaling pathways. Based on their size, intracellular origin, and secretion pathway, EVs have been grouped into three main populations: exosomes, microvesicles (or microparticles), and apoptotic bodies. Several molecules can be found inside MSC-derived EVs, including proteins, lipids, mRNA, microRNAs, DNAs, as well as organelles that can be transferred to damaged recipient cells, thus contributing to the reparative process and promoting relevant anti-inflammatory/resolutive actions. Indeed, the paracrine/endocrine actions induced by MSC-derived EVs have demonstrated therapeutic potential to mitigate or even reverse tissue damage, thus raising interest in the regenerative medicine field, particularly for lung diseases. In this review, we summarize the main features of EVs and the current understanding of the mechanisms of action of MSC-derived EVs in several lung diseases, such as chronic obstructive pulmonary disease (COPD), pulmonary infections [including coronavirus disease 2019 (COVID-19)], asthma, acute respiratory distress syndrome (ARDS), idiopathic pulmonary fibrosis (IPF), and cystic fibrosis (CF), among others. Finally, we list a number of limitations associated with this therapeutic strategy that must be overcome in order to translate effective EV-based therapies into clinical practice.