The digitization of manufacturing has transformed the product realization process across many industries, from aerospace and automotive to medicine and healthcare. While this progress has accelerated product development cycles and enabled designers to create products with previously unachievable complexity and precision, it has also opened the door to a broad array of unique security concerns, from theft of intellectual property to supply chain attacks and counterfeiting. To address these concerns, information embedding (e.g., watermarks and fingerprints) has emerged as a promising solution that enhances product security and traceability. Information embedding techniques involve storing unique and secure information within parts, making these parts easier to track and to verify for authenticity. However, a successful information embedding scheme requires information to be transmitted in physical parts both securely and in a way that is accessible to end users. Ensuring these qualities introduces unique computational and engineering challenges. For instance, these qualities require the embedding scheme designer to have an accurate model of the cyber-physical processes needed to embed information during manufacturing and read that information later in the product life cycle, as well as models of the cyber-physical, economic, and/or industrial processes that may degrade that information through natural wear-and-tear, or through intentional attacks by determined adversaries. This paper discusses challenges and research opportunities for the engineering design and manufacturing community in developing methods for efficient information embedding in manufactured products.