There's also a level above that, where you're aware of what is aware. I find this mental state to be even more calming/grounding than being aware of breathing but I'm not always able to shift myself into it. Being aware of breathing feels much easier/natural to me whenever I'm able to remind myself of it, which already provides quite a noticeable effect on how I'm feeling and reacting to whatever is happening in that moment.
Additionally, there's a practice called "walking meditation" [0] that can also be useful to practice this area of skills.