A tiny fraction (<1%) of very metal-deficient (12+log(O/H)≤7.6) blue compact dwarf (BCD) galaxies exhibits a nearly galaxy-wide starburst activity and no signatures of an old stellar host galaxy. The evolutionary status and formation history of these most metal-deficient BCDs are still a subject of debate. Various lines of evidence suggest, however, that these systems do not contain a substantial population of stars older than $\sim$1 Gyr and hence qualify as nearby young-galaxy candidates. Elaborated multiwavelength studies of these rare, most metal-deficient BCDs may therefore provide crucial insights into the formation and starburst-driven evolution of low-mass galaxies in the early universe.