SPL (SQUAMOSA promoter binding protein-like), as one family of plant transcription factors, plays an important function in plant growth and development and in response to environmental stresses. Despite SPL gene families having been identified in various plant species, the understanding of this gene family in peanuts remains insufficient. In this study, thirty-eight genes (AhSPL1-AhSPL38) were identified and classified into seven groups based on a phylogenetic analysis. In addition, a thorough analysis indicated that the AhSPL genes experienced segmental duplications. The analysis of the gene structure and protein motif patterns revealed similarities in the structure of exons and introns, as well as the organization of the motifs within the same group, thereby providing additional support to the conclusions drawn from the phylogenetic analysis. The analysis of the regulatory elements and RNA-seq data suggested that the AhSPL genes might be widely involved in peanut growth and development, as well as in response to environmental stresses. Furthermore, the expression of some AhSPL genes, including AhSPL5, AhSPL16, AhSPL25, and AhSPL36, were induced by drought and salt stresses. Notably, the expression of the AhSPL genes might potentially be regulated by regulatory factors with distinct functionalities, such as transcription factors ERF, WRKY, MYB, and Dof, and microRNAs, like ahy-miR156. Notably, the overexpression of AhSPL5 can enhance salt tolerance in transgenic Arabidopsis by enhancing its ROS-scavenging capability and positively regulating the expression of stress-responsive genes. These results provide insight into the evolutionary origin of plant SPL genes and how they enhance plant tolerance to salt stress.