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Inflation that is fully anticipated has few real effects in purely private market economies, but this need not be the case in the presence of taxation. In practice, tax systems are not neutral with respect to inflation - though some countries have attempted make their tax systems inflation-neutral in the past - and this paper provides a comprehensive overview of the most relevant non-neutralities, drawing on existing literature, but also supplying new illustrations and evidence of the effects. The paper shows, for example, how taxing inflationary gains can have a large impact on effective tax rates - even at relatively low rates of inflation. It also shows how partial coverage of protection against inflation - for some types of incomes only - can create additional distortions. A new empirical analysis reveals how the erosion of the value of depreciation allowances through inflation affects investment. Finally, the paper discusses policy options to address such non-neutralities.