The Lyman-alpha (Lyα) line is the strongest recombination line of hydrogen, which constitutes the dominant share of normal matter in the Universe. Fifty-one years ago, it was predicted that Lyα emission should appear prominently in the spectra of young primordial galaxies. For the next 30 years, this prediction was tested by many surveys, but none found the predicted galaxies at the predicted luminosities. The blame for these non-detections was squarely cast on the resonant nature of the Lyα line, which requires Lyα photons to scatter off many hydrogen atoms before escaping from a galaxy. This can hugely increase the path that they traverse, and consequently also the probability that they will be absorbed by dust. This remained the dominant explanation of the missing high-redshift lines for decades, despite some dissenting opinions about the effect of dust. The spectra of nearby galaxies from the International Ultraviolet Explorer are inconclusive about what allows galaxies to be Lyα emitters. The ‘missing’ lines were finally detected 20 years ago, at flux levels much below the original predictions - a difference that we understand to be predominantly due to the hierarchical growth of galaxies, such that star-forming objects at high redshift are much less massive than anticipated in the original prediction. The discovery and study of Lyα galaxies has blossomed into an invaluable method for understanding the youngest stages of galaxy formation, the circumgalactic medium, and ultimately the epoch of reionization. The high equivalent widths of Lyα galaxies from the earliest high-redshift surveys show that they are low-mass galaxies dominated by young stellar populations. The Sakura CLAW workshop (which used the Twitter hashtag #SakuraCLAW) gathered more than 110 participants (Fig. 1) who showcased progress that pushed the frontiers of Lyα galaxy science in sample size, sensitivity, redshifts and physical understanding..
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