Japanese convenience stores may have been born in the United States (two of the three biggest chains in Japan, 7-11 and Lawson, are originally from the US), but they came into their own in Japan. While convenience stores in the US are known mostly for beef jerky, Red Bull, and not much else, konbini in Japan are actually convenient, offering a wide array of products and services for only a slight premium over what they might cost in bigger, less convenient stores.
The first modern-style chain stores opened in the 1970s. Before that, there were scattered corner stores; dagashiya (candy and snack stores, often with simple toys, aimed mostly at children); and tabakoya (cigarette shops) since at least the late 1800s. However, with the rise of konbini, these kinds of specialty stores have been largely crushed. Over the last few decades, konbini steadily proliferated, incorporated into hospitals, city halls, hotels, and office buildings, becoming an ubiquitous part of Japan.
Insider tip: Most konbini are open 24 hours a day, though there are exceptions for those that are part of larger buildings or businesses with shorter hours.