Both free markets and government regulators tend to use willingness to pay (WTP) as the measure of value of goods that people do not own, and willingness to accept (WTA) as the measure of value of goods that people do own. The challenge is that WTP and WTA are not perfect proxies for the welfare effects of buying or selling goods, especially when people do not have experience with those goods. The reason for use of WTP and WTA is not that they are perfect, but that they count as the best and the most administrable methods for capturing the relevant welfare effects. At the same time, WTP and WTA might be infected by a lack of information, by behavioral biases, and by hedonic forecasting errors (all of which might be either cured or aggravated by market processes). Challenges also arise when WTP is low because people do not have money and when distributional weights might be necessary to align WTP or WTA with welfare effects. There are questions about how to proceed when WTA is much higher than WTP for the same goods; the WTP-WTA disparity has yet to be fully understood. These questions are especially challenging when valuing environmental amenities, animal welfare, and social media. Some ways are offered to meet these challenges.