The Canadian Test-Day Model is a 12-trait random regression animal model in which traits are milk, fat, and protein test-day yields, and somatic cell scores on test days within each of first three lactations. Test-day records from later lactations are not used. Random regressions (genetic and permanent environmental) were based on Wilmink's three parameter function that includes an intercept, regression on days in milk, and regression on an exponential function to the power -0.05 times days in milk. The model was applied to over 22 million test-day records of over 1.4 million cows in seven dairy breeds for cows first calving since 1988. A theoretical comparison of test-day model to 305-d complete lactation animal model is given. Each animal in an analysis receives 36 additive genetic solutions (12 traits by three regression coefficients), and these are combined to give one estimated breeding value (EBV) for each of milk, fat, and protein yields, average daily somatic cell score and milk yield persistency (for bulls only). Correlation of yield EBV with previous 305-d lactation model EBV for bulls was 0.97 and for cows was 0.93 (Holsteins). A question is whether EBV for yield traits for each lactation should be combined into one overall EBV, and if so, what method to combine them. Implementation required development of new methods for approximation of reliabilities of EBV, inclusion of cows without test day records in analysis, but which were still alive and had progeny with test-day records, adjustments for heterogeneous herd-test date variances, and international comparisons. Efforts to inform the dairy industry about changes in EBV due to the model and recovering information needed to explain changes in specific animals' EBV are significant challenges. The Canadian dairy industry will require a year or more to become comfortable with the test-day model and to realize the impact it could have on selection decisions.