Voids occupy about 3/4 of the volume of the Universe and contain about 15% of its mass. Due to various observational selection effects, these structure elements and galaxies populating voids, are highly under-explored. This especially relates to the lowest mass galaxies which comprise the main void population. Studying the nearby voids allows us to improve our understanding of the most elusive void objects. We present a brief overview of the current status and prospects of the study of nearest voids and their galaxies. First, we summarize the pioneer study of a hundred galaxies residing in the nearby Lynx-Cancer void, which clearly evidences for the slower evolution of void galaxies and also finds the unusual very metal-poor and gas-rich dwarfs. Then we describe the recently defined sample of the nearby voids within a sphere with R = 25 Mpc and a sample of 1350 galaxies residing in these voids ($\sim$20% of all galaxies within this volume). We discuss the current results obtained for several directions of the study of this sample. They include: the search for Very Young Galaxies, the study of HI properties, the clustering of void galaxies and its relation to the void substructures, and the unbiased study of 260 void galaxies within the Local Volume (R $<$ 11 Mpc). Altogether, this opens a promising way to address the suggested peculiarities of void galaxy formation and evolution. Finally, we briefly overview the expected advancements in the void galaxy studies related to the upcoming new facilities.