•The age-adjusted incidence rate (AAIR) of thyroid cancer nearly tripled between 1980 and 2014.•The AAIR increased for papillary carcinomas (quintupled) and follicular carcinomas (tripled).•Papillary carcinomas had the best overall survival and anaplastic carcinomas had the worst.•There was identified an age-effect on the incidence of thyroid cancer but not a period or cohort effectt. Thyroid cancer incidence has been reported to be increasing since the 1970 s. The aim of this study was to investigate the change in incidence and survival from 1980 to 2014 in Denmark. We identified patients registered with thyroid cancer in the period 1980–2014. We evaluated the age-adjusted incidence rate (AAIR) and the average annual percentage change (AAPC), constructed age–period–cohort models (APCs), and evaluated relative survival (RS). We included 5139 patients. The AAIR was 1.6 cases per 100,000 in 1980 and 4.5 cases in 2014 with an AAPC of 3.4%. The AAIR for papillary carcinomas (n = 2864) quintupled in the study period, and accounts for most of the observed increase in incidence with an AAPC of 4.9%. Follicular carcinomas (n = 920) nearly tripled in AAIR and had the second greatest increase in AAPC. Papillary carcinomas had the best prognosis with 1-year and 5-year RSs of 95% and 91%, followed by the follicular carcinomas with 1-year and 5-year RSs of 90% and 80%, respectively. Anaplastic carcinomas (n = 320) had the worst prognosis with 1-year and 5-year RSs of 18% and 12%. We found a significant age effect in the APC model for the incidence of thyroid cancer but no significant cohort or period effects. The incidence of thyroid cancer is rising. This is primarily attributable to an increase in papillary carcinomas. The relative survival has improved significantly in Denmark since 1980. The cause of the increasing incidence remains to be established, but enhanced diagnostic scrutiny and increased iodine intake may be influential.