Rather surprisingly, to anyone who is most familiar with textbook mitochondria, many simple single-celled eukaryotes have mitochondria that operate in the absence of oxygen. Instead of using oxygen to burn up food, these 'anaerobic' mitochondria use other simple compounds like nitrate or nitrite. In most other respects, they operate in a very similar fashion to our own mitochondria, and are unquestionably related. So the spectrum stretches from aerobic mitochondria like our own, which are dependent on oxygen, through 'anaerobic' mitochondria, which prefer to use other molecules like nitrates, to the hydrogenosomes, which work rather differently but are still related.