The regulatory takings problem is easy to describe but difficult to resolve. The government enacts restrictions on land use that reduce the market value of the targeted parcels by a considerable amount. The restrictions are couched in terms of the police power, but actually they might amount to a taking that requires compensation, not because any of the land has been wrested away (it hasn't), but because much of the value has. Through the police power the government gets to govern for free, whereas with takings it's pay as you go. On what does the distinction-police power or taking-depend?
Krier, James E. "Takings from Freund to Fischel." Review of Regulatory Taking: Law, Economics, and Politics, by W. A. Fischel. Geo. L. J. 84, no. 5 (1996): 1895-911.