As machine learning (ML) techniques and sensor technology continue to gain importance, the data-driven perspective has become a relevant approach for improving the quality of maintenance for machines and processes in industrial environments. Our study provides an analytical literature review of existing industrial maintenance strategies showing first that, among all existent approaches to maintenance, each varying in terms of efficiency and complexity, predictive maintenance best fits the needs of a highly competitive industry setup. Predictive maintenance is an approach that allows maintenance actions to be based on changes in the monitored parameters of the assets by using a variety of techniques to study both live and historical information to learn prognostic data and make accurate predictions. Moreover, we argue that, in any industrial setup, the quality of maintenance improves when the applied data-driven techniques and methods (i) have economic justifications and (ii) take into consideration the conformity with the industry standards. Next, we consider ML to be a prediction methodology, and we show that multimodal ML methods enhance industrial maintenance with a critical component of intelligence: prediction. Based on the surveyed literature, we introduce taxonomies that cover relevant predictive models and their corresponding data-driven maintenance techniques. Moreover, we investigate the potential of multimodality for maintenance optimization, particularly the model-agnostic data fusion methods. We show the progress made in the literature toward the formalization of multimodal data fusion for industrial maintenance.