The endocannabinoid retrograde signaling pathway is widely expressed in the central nervous system, where it plays major roles in regulating synaptic plasticity (excitatory and inhibitory) through long-term potentiation and long-term depression. The endocannabinoid system (ECS) components—cannabinoid receptors, endocannabinoids and synthesis/degradation enzymes—are expressed and are functional from early developmental stages and throughout adolescent cortical development, regulating progenitor cell fate, neural differentiation, migration and survival. This may potentially confer increased vulnerability to adverse outcomes from early cannabinoid exposure. Cannabidiol (CBD) is one of the most studied exogenous cannabinoids, and CBD-enriched Cannabis extracts have been widely (and successfully) used as adjuvants to treat children with refractory epilepsy, and there is even a Food and Drug Administration (FDA)-approved drug with purified CBD derived from Cannabis. However, there is insufficient information on possible long-term changes in the central nervous system caused by cannabinoid treatments during early childhood. Like the majority of cannabinoids, CBD is able to exert its effects directly and indirectly through the ECS, which can perturb the regulatory processes mediated by this system. In addition, CBD has a large number of non-endocannabinoid targets, which can explain CBD’s effects. Here, we review the current knowledge about CBD-based therapies—pure and CBD-enriched Cannabis extracts—in studies with pediatric patients, their side effects, and their mechanisms of action regarding the central nervous system and neurodevelopment aspects. Since Cannabis extracts contain Δ9-tetrahydrocannabinol (Δ9-THC), we consider that pure CBD is possibly safer for young patients. Nevertheless, CBD, as well as other natural and/or synthetic cannabinoids, should be studied in more detail as a therapeutic alternative to CBD-enriched Cannabis extracts for young patients.