Copy number variants (CNVs), defined as genome sequences of ≥50 bp that differ in copy number from that in a reference genome, are a common form of structural variation. Germline CNVs account for some of the missing heritability that single nucleotide polymorphisms could not account for. Recent technological advances have had a huge impact on CNV research. Microarray technology enables relatively low-cost, high-throughput, genome-wide measurements, and short-read sequencing technology enables the detection of short CNVs that cannot be detected by microarrays. As a result, large-scale genetic studies have been able to identify a variety of common and rare germline CNVs and their associations with diseases. Rare germline CNVs have been reported to be associated with neuropsychiatric disorders. In this review, we focused on germline CNVs and briefly described their functional characteristics, formation mechanisms, detection methods, related databases, and the latest findings. Finally, we introduced recent large-scale genetic studies to assess associations of CNVs with diseases, especially psychiatric disorders, and discussed the use of CNV-based animal models to investigate the molecular and cellular mechanisms underlying these disorders. The development and implementation of improved detection methods, such as long-read single-molecule sequencing, are expected to provide additional insight into the molecular basis of psychiatric disorders and other complex diseases, thus facilitating basic and clinical research on CNVs.