We study optimal investment and the valuation of assets whose payouts cannot be replicated by trading other assets. Our market model allows for constraints and illiquidity effects that are encountered in practice. We review two hedging-based notions of asset value and relate them to the classical notions of risk neutral and net present values. Many classical results e.g. on attainability and duality are extended to the illiquid market setting. This is joint work with Ari-Pekka Perkkiö.