The impact of copy-number variations (CNVs) on complex human traits remains understudied. We called CNVs in 331,522 UK Biobank participants and performed genome-wide association studies (GWASs) between the copy number of CNV-proxy probes and 57 continuous traits, revealing 131 signals spanning 47 phenotypes. Our analysis recapitulated well-known associations (e.g., 1q21 and height), revealed the pleiotropy of recurrent CNVs (e.g., 26 and 16 traits for 16p11.2-BP4-BP5 and 22q11.21, respectively), and suggested gene functionalities (e.g., MARF1 in female reproduction). Forty-eight CNV signals (38%) overlapped with single-nucleotide polymorphism (SNP)-GWASs signals for the same trait. For instance, deletion of PDZK1, which encodes a urate transporter scaffold protein, decreased serum urate levels, while deletion of RHD, which encodes the Rhesus blood group D antigen, associated with hematological traits. Other signals overlapped Mendelian disorder regions, suggesting variable expressivity and broad impact of these loci, as illustrated by signals mapping to Rotor syndrome (SLCO1B1/3), renal cysts and diabetes syndrome (HNF1B), or Charcot-Marie-Tooth (PMP22) loci. Total CNV burden negatively impacted 35 traits, leading to increased adiposity, liver/kidney damage, and decreased intelligence and physical capacity. Thirty traits remained burden associated after correcting for CNV-GWAS signals, pointing to a polygenic CNV architecture. The burden negatively correlated with socio-economic indicators, parental lifespan, and age (survivorship proxy), suggesting a contribution to decreased longevity. Together, our results showcase how studying CNVs can expand biological insights, emphasizing the critical role of this mutational class in shaping human traits and arguing in favor of a continuum between Mendelian and complex diseases.