Corporation taxes are under pressure from a number of sources. This paper looks at the arguments for and against corporation tax in the context of Australia, which has had for 30 years a dividend imputation system for corporate-shareholder taxation. Corporation tax is estimated to have a high economic cost relative to the revenue raised; there are worries about base erosion and profit shifting (BEPS); and there are suggestions that dividend imputation should be abolished to allow a lower corporate tax rate. The imputation system and discount for capital gains tax largely eliminates the corporation tax for Australian domestic investors, so that the effective tax on domestic corporate investment is indicated by personal income and capital gains taxes. Hence the Australian corporation tax is mainly a tax on foreign investment. In an era of mobile international capital this role is increasingly problematic. In the long run, the corporation tax may wither away due to international tax competition and BEPS. This may be an acceptable development provided that, as this happens, we put in place a stronger system of personal taxation of capital incomes, with international co-operation in the discovery and valuation of such incomes. We can also rely on consumption tax, such as the Goods and Services Tax (GST), or a business cash flow tax, to tax part of corporate sector economic rents.