The Scandinavian welfare states are mature in the sense of having a high level of standards for public provisions of welfare services as well as a high replacement level for income transfers, especially for low income groups. In this welfare model, individuals have basic rights to welfare services and social transfers independently of their ability to pay, their labour market history etc. The financial viability of the model relies on a high tax burden and a high level of labour force participation for males and females. Evaluated on the basis of international comparisons of income levels and inequality, the model has performed well. In a forward looking perspective, however, the welfare model faces problems that may bring the financial viability of the model at stake. Two important challenges are demographic changes and the so-called growth dilemma (increased demand for services and leisure). We discuss these issues using Denmark as an example and argue that while these two challenges may be of the same order of magnitude, it is easier to propose solutions to the demographic challenges than to the growth dilemma which are consistent with the basic principles of the welfare state.