Hydrogel materials have been employed as biological scaffolds for tissue regeneration across a wide range of applications. Their versatility and biomimetic properties make them an optimal choice for treating the complex and delicate milieu of neural tissue damage. Aside from finely tailored hydrogel properties, which aim to mimic healthy physiological tissue, a minimally invasive delivery method is essential to prevent off-target and surgery-related complications. The specific class of injectable hydrogels termed self-assembling peptides (SAPs), provide an ideal combination of in situ polymerization combined with versatility for biofunctionlization, tunable physicochemical properties, and high cytocompatibility. This review identifies design criteria for neural scaffolds based upon key cellular interactions with the neural extracellular matrix (ECM), with emphasis on aspects that are reproducible in a biomaterial environment. Examples of the most recent SAPs and modification methods are presented, with a focus on biological, mechanical, and topographical cues. Furthermore, SAP electrical properties and methods to provide appropriate electrical and electrochemical cues are widely discussed, in light of the endogenous electrical activity of neural tissue as well as the clinical effectiveness of stimulation treatments. Recent applications of SAP materials in neural repair and electrical stimulation therapies are highlighted, identifying research gaps in the field of hydrogels for neural regeneration.