Carcass and price traits of 72,969 Hanwoo cows, bulls and steers aged 16 to 80 months at slaughter collected from 2002 to 2013 at 75 beef packing plants in Korea were analyzed to determine heritability, correlation and breeding value using the Multi-Trait restricted maximum likelihood (REML) animal model procedure. The traits included carcass measurements, scores and grades at 24 h postmortem and bid prices at auction. Relatively high heritability was found for maturity ($0.41{\pm}0.031$), while moderate heritability estimates were obtained for backfat thickness ($0.20{\pm}0.018$), longissimus muscle (LM) area ($0.23{\pm}0.020$), carcass weight ($0.28{\pm}0.019$), yield index ($0.20{\pm}0.018$), yield grade ($0.16{\pm}0.017$), marbling ($0.28{\pm}0.021$), texture ($0.14{\pm}0.016$), quality grade ($0.26{\pm}0.016$) and price/kg ($0.24{\pm}0.025$). Relatively low heritability estimates were observed for meat color ($0.06{\pm}0.013$) and fat color ($0.06{\pm}0.012$). Heritability estimates for most traits were lower than those in the literature. Genetic correlations of carcass measurements with characteristic scores or quality grade of carcass ranged from -0.27 to +0.21. Genetic correlations of yield grade with backfat thickness, LM area and carcass weight were 0.91, -0.43, and -0.09, respectively. Genetic correlations of quality grade with scores of marbling, meat color, fat color and texture were -0.99, 0.48, 0.47, and 0.98, respectively. Genetic correlations of price/kg with LM area, carcass weight, marbling, meat color, texture and maturity were 0.57, 0.64, 0.76, -0.41, -0.79, and -0.42, respectively. Genetic correlations of carcass price with LM area, carcass weight, marbling and texture were 0.61, 0.57, 0.64, and -0.73, respectively, with standard errors ranging from ${\pm}0.047$ to ${\pm}0.058$. The mean carcass weight breeding values increased by more than 8 kg, whereas the mean marbling scores decreased by approximately 0.2 from 2000 through 2009. Overall, the results suggest that genetic improvement of productivity and carcass quality could be obtained under the national scale breeding scheme of Korea for Hanwoo and that continuous efforts to improve the breeding scheme should be made to increase genetic progress.