Univalent Na- and multivalent (Ca, Mg, Al)- ion batteries have recently emerged as potential candidates to replace Li-ion batteries in some applications. Their elemental natural abundance, homogeneous geographic distribution and high volumetric capacities in some cases, could be useful for this purpose. However, Li-ion batteries could still show notorious improvements in fields such as miniaturization, integration in electronic circuits, enhanced energy densities and improved safety. In this talk, several recent developments achieved at our laboratory regarding these topics as well yet unsolved challenges will be discussed. High nergy-density miniaturized Li-ion batteries, together with Na-, Mg-, Ca- and Al-ion test batteries will be discussed, with special emphasis on the problems associated to their use that will require further analysis and development.