With the growing global population, the need for food is expected to grow tremendously in the next few decades. One of the key tools to address such growing food demand is minimizing grain losses and optimizing food processing operations. Hence, several research studies are underway to reduce grain losses/degradation at the farm (upon harvest) and later during the milling and baking processes. However, less attention has been paid to changes in grain quality between harvest and milling. This paper aims to address this knowledge gap and discusses possible strategies for preserving grain quality (for Canadian wheat in particular) during unit operations at primary, process, or terminal elevators. To this end, the importance of wheat flour quality metrics is briefly described, followed by a discussion on the effect of grain properties on such quality parameters. This work also explores how drying, storage, blending, and cleaning, as some of the common post-harvest unit operations, could affect grain's end-product quality. Finally, an overview of the available techniques for grain quality monitoring is provided, followed by a discussion on existing gaps and potential solutions for quality traceability throughout the wheat supply chain.