An heirloom tomato is an open-pollinated variety which has either been passed down from generations of people or was introduced commercially before the 1940s. Open-pollinated fruits are "stable," their fruit seeds will produce identical offspring, as long as some precautions are taken.
While their stability was agriculturally beneficial, heirloom tomatoes were phased out from commercial agriculture in favor of modified tomato varieties which could produce heavier, more uniform, and pest-resistant yields at a faster rate.
However, these ubertomatoes lacked the sweet juicy "good ol' tomato" flavor of their heirloom counterparts, leading to increased consumer interest in heirloom tomatoes. While many varieties of heirloom tomatoes have been lost to time, many have also been preserved, on small family farms, in collections, and through Indigenous agricultural practices. Some of the most common heirloom tomatoes are Brandywine, San Marzano, and Amish Paste. And, as people have begun to seek out heirloom tomatoes, old varieties have resurfaced, the most iconic example being the Cherokee Purple, rediscovered in 1990.
Heirloom tomatoes can be found at farmer's markets and local grocery stores, when and where in-season. More "exotic" varieties may be encountered through exploration and adventure.
Finally, a disclaimer:
Many so-called "heirloom tomatoes" carried at large supermarket chains are hybrids, at best.
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Sources:
Weidman, A. (2016, September 13). Heirloom tomatoes: The “cherokee purple” – mother earth gardener. Mother Earth Gardener – Expert advice on all aspects of growing and using historic fruit and vegetable cultivars, along with fiber, ornamental, and medicinal plants. https://www.motherearthgardener.com/plant-profiles/heirloom-tomatoes-cherokee-purple-zmaz12fzfis/
Division of Agriculture and Natural Resources. (n.d.). Heirloom Tomatoes . UC Master Gardeners of Sacramento. https://sacmg.ucanr.edu/What_are_Heirloom_Tomatoes/