All three practices are linked. In order to practice mindfulness and meditation, you benefit from deep breathwork for an extended period. If you want to practice meditation, you benefit from being mindful.
Mindfulness can be practiced anywhere at any time, doing practically anything. This involves focusing on the present moment in detail. It also serves to reduce stress and promote inner peace among other benefits.
Deep breathwork is the foundation for mindfulness and meditation. It is typically how a meditation would start. However, breathwork can also be used to bring awareness of the breath into the conscious mind.
In this latter example, I find I can use deep breathing to take back control of emotions that can affect my ability to perform. I used to use this at work all the time. I manage my own anxiety, so I would often find that before the start of a new group I would feel anxious. Likewise, I would find in meetings and training sessions my anxiety would spike as I became aware it was my turn to contribute. In these instances, I would use deep breathing to bring awareness to my breath and manage the breathing. Once I had detected my breathing was erratic, I could focus on deep breathing exercises to control my breathing.
The exercises would control my breathing, which in turn would lower my heart rate, and I could then focus on responding to the situation. Once these physical symptoms were under control, I found I could think more clearly and be mindful in the moment.
Although the benefits of extended deep breathwork are undeniable, it can also be used to bring the breathing back under control in a short space of time. As such it is so valuable because you can do it anywhere at any time, and no one needs to know you are doing it.