Knowledge Graphs (KGs) are large collections of structured data that can model real world knowledge and are important assets for the companies that employ them. KGs are usually constructed iteratively and often show a sparse structure. Also, as knowledge evolves, KGs must be updated and completed. Many automatic methods for KG Completion (KGC) have been proposed in the literature to reduce the costs associated with manual maintenance. Motivated by an industrial case study aiming to enrich a KG specifically designed for Natural Language Understanding tasks, this paper presents an overview of classical and modern deep learning completion methods. In particular, we delve into Large Language Models (LLMs), which are the most promising deep learning architectures. We show that their applications to KGC are affected by several shortcomings, namely they neglect the structure of KG and treat KGC as a classification problem. Such limitations, together with the brittleness of the LLMs themselves, stress the need to create KGC solutions at the interface between symbolic and neural approaches and lead to the way ahead for future research in intelligible corpus-based KGC
