Lyman-alpha emitters (LAEs) are young galaxies that are actively forming new stars. They glow brightly in a specific type of ultraviolet (UV) light known as Lyman-alpha radiation, which comes from hydrogen gas surrounding hot, young stars. Studying LAEs helps us understand how young, massive stars form and how the early universe transitioned from a foggy state—filled with neutral hydrogen—to a clear one where light could travel freely. This clearing process, called reionization, was driven by the energy released from the first stars and galaxies. In this talk, I will discuss what we have learned about the morphology and star-forming regions of LAEs. We find that most LAEs are compact, meaning their star-forming areas are small and densely packed. This compactness may help Lyman-alpha light escape more easily by creating holes in the gas, likely caused by powerful winds and radiation from massive stars. I will also highlight a special case: the Sunburst Arc, a strongly lensed LAE. Gravitational lensing allows us to observe it in fine detail. This galaxy emits not only Lyman-alpha light but also Lyman-continuum radiation, which played a key role in reionization. This radiation appears to escape from a single, extreme star cluster with features such as very blue light and high ionization. It suggests that this light escapes through narrow paths rather than evenly in all directions. By studying galaxies like these, we get closer to understanding how the early universe became transparent and how the first galaxies influenced cosmic history.