<p>Over the past years, embedding learning on networks has shown tremendous results in link prediction tasks for complex systems, with a wide range of real-life applications. Learning a representation for each node in a knowledge graph allows us to capture topological and semantic information, which can be processed in downstream analyses later. In the link prediction task, high-dimensional network information is encoded into low-dimensional vectors, which are then fed to a predictor to infer new connections between nodes in the network. As the network complexity (that is, the numbers of connections and types of interactions) grows, embedding learning turns out increasingly challenging. This review covers published models on embedding learning on multiplex networks for link prediction. First, we propose refined taxonomies to classify and compare 38 models (in 36 papers) across five methodological categories and three embedding classes. Second, we review and address the problem of reproducible and fair evaluation of embedding learning on multiplex networks for the link prediction task. Finally, we highlight challenges specific to performance evaluation on directed multiplex networks, and address them by introducing a novel and fair testing procedure. This review constitutes a crucial step towards the development of more performant and tractable embedding learning approaches for multiplex networks and their fair evaluation for the link prediction task. We also suggest guidelines on the evaluation of models, and provide an informed perspective on the challenges and tools currently available to address downstream analyses applied to multiplex networks.</p>