Crop yield improvement is essential for feeding the growing world population without concomitant increases in land allocated to agriculture. Oil crops are critical components of food supply as well as non-food applications. Oil palm is of particular value due to its significantly higher yield per unit area of land as compared to other oil crops. In the context of sustainable production of edible oils, this review will discuss the role of biochemical-omics techniques, including metabolomics, transcriptomics and proteomics research for yield improvement through plant breeding; in particular, the unique challenges of the mesocarp-oil bearing perennial crop, oil palm, are specifically discussed along with perspectives on what is needed for future crop improvement. Future oil crop improvement will need to go beyond classical trait selection, and omics research needs to go beyond looking at oil biosynthesis and fruit development. We need to explore carbon supply and flux, plant stress response, nutrient uptake and water use through a combination of genetics, biochemistry, epigenetics and gene interaction coupled to more detailed and continuous phenotypic data analysis.