The seed oils of domesticated oilseed crops are major agricultural commodities that are used primarily for nutritional applications, but in recent years there has been increasing use of these oils for production of biofuels and chemical feedstocks. This is being driven in part by the rapidly rising costs of petroleum, increased concern about the environmental impact of using fossil oil, and the need to develop renewable domestic sources of fuel and industrial raw materials. There is also a need to develop sustainable sources of nutritionally important fatty acids such as those that are typically derived from fish oil. Plant oils can provide renewable sources of high-value fatty acids for both the chemical and health-related industries. The value and application of an oil are determined largely by its fatty acid composition, and while most vegetable oils contain just five basic fatty acid structures, there is a rich diversity of fatty acids present in nature, many of which have potential usage in industry. In this review, we describe several areas where plant oils can have a significant impact on the emerging bioeconomy and the types of fatty acids that are required in these various applications. We also outline the current understanding of the underlying biochemical and molecular mechanisms of seed oil production, and the challenges and potential in translating this knowledge into the rational design and engineering of crop plants to produce high-value oils in plant seeds.