Fascial plane blocks (FPBs) are regional anesthesia techniques in which the space (“plane”) between two discrete fascial layers is the target of needle insertion and injection. Analgesia is primarily achieved by local anesthetic spread to nerves traveling within this plane and adjacent tissues. This narrative review discusses key fundamental anatomical concepts relevant to FPBs, with a focus on blocks of the torso. Fascia, in this context, refers to any sheet of connective tissue that encloses or separates muscles and internal organs. The basic composition of fascia is a latticework of collagen fibers filled with a hydrated glycosaminoglycan matrix and infiltrated by adipocytes and fibroblasts; fluid can cross this by diffusion but not bulk flow. The plane between fascial layers is filled with a similar fat-glycosaminoglycan matric and provides gliding and cushioning between structures, as well as a pathway for nerves and vessels. The planes between the various muscle layers of the thorax, abdomen, and paraspinal area close to the thoracic paravertebral space and vertebral canal, are popular targets for ultrasound-guided local anesthetic injection. The pertinent musculofascial anatomy of these regions, together with the nerves involved in somatic and visceral innervation, are summarized. This knowledge will aid not only sonographic identification of landmarks and block performance, but also understanding of the potential pathways and barriers for spread of local anesthetic. It is also critical as the basis for further exploration and refinement of FPBs, with an emphasis on improving their clinical utility, efficacy, and safety.