In their native Japan, they have long served as a snacking item - often served stem-on as a finger food. It is common to skewer them for roasting over an open fire. Cooking brings out a smoky flavor. Only since the early 2000s have they become more available in locales throughout the world, including farmer's markets and restaurants(1).
Raw, they can top salads and otherwise serve as condiments. Poking a hole in the pepper prevents expanding hot air from it blowing apart when cooking(2). Pickling is another option. Shishitos blister easier than most chiles. Simple oil and sea salt is a most common preparation. Yet, they complement many flavors as cilantro, citrus, garlic, olive oil, seafood, and creamy sauces among others(1). [Really, in many respects, they can be eaten like many other peppers.]
Sources:
1. "Green Shishito Chile Peppers." Specialty Produce, Web 16 October 2019. https://www.specialtyproduce.com/produce/Green_Shishito_Chile_Peppers_139.php.
2. Wikipedia contributors. "Shishito." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, Updated 26 Aug. 2019. Web 16 Oct. 2019. https://en.wikipedia.org/wiki/Shishito