Topical issues in petroleum tax design are in this chapter discussed by means of a tax model for anet income tax system (Norway) and a representative PSA regime. We analyse the entire lifecycle of a typical petroleum project, i.e., the exploration decision is included. Many petroleumtax systems are regressive, and thus not able to cope with high increases or decreases in the oilprice. Accordingly, many countries are seeking to include progressive elements in their taxsystem. We discuss the trade-off between progressivity on the one hand and the optimal sharingof risk and investment between the oil companies and the host government on the other. Optimalrisk sharing and optimal allocation of cash flow over the project lifetime between hostgovernment and international oil company, often call for the oil company to fund the initialinvestments. The high front end loading of costs and the high risk on part of the oil company,calls for it to keep a substantial part of the upside if the project is successful...