This chapter provides a critical survey of some of the main contributions proposed in the optimal control theory to compute the economic depreciation of natural resources analytically and thus arrive at a correct welfare measure. It examines the issue of the accounting prices that can be used to determine the economic depreciation of natural capital. The chapter explores the treatment of environmental defensive expenditures since different theoretical models take different approaches to this issue. National accountants have extended the System of National Accounts in the form of satellite accounts, the main result being the System of Economic and Environmental Accounts proposed by the United Nations in 1993. Surprisingly enough, most of the debate on environmental accounting started with a seminal paper by M. Weitzman which contained no reference to environmental issues. One possibility is to use defensive expenditures as an approximation of environmental damage and subtract them from the accounts.