A lot of women, specifically postpartum, ask about one thing in particular: belly binders. There's a lot of conflicting information out there about this. They're called different things like "waist trainers," "corsets," "binders," "belly bands," "support bands," etc. but they all serve the same purpose: to help shrink the waistline. Or at least, that's what they're supposed to do..
There is certainly a time and place for putting these to use, first of all being immediately postpartum. After giving birth, your core may feel like its literally falling apart. A support binder may help to make you feel more stable for the first 1-3 weeks while your body initially starts shifting into a more functional position. A good postpartum support is one that is breathable, stretchy, not too stiff (like a corset), and feels more like a large bandage than a brace.
In regards to using one during exercise, the general feeling I have is if you need the support band to do the exercise, than you shouldn't be doing that movement. Period. The real solution here is to focus on rebuilding strength in your transverse abdominus and pelvic floor. This can be done with help from a women's pelvic floor health specialist, a physio, or a physical therapist, in addition to working with a trainer who is knowledgeable and certified in this area.
However, this should really just be a temporary support. If you continue to use the band past the 4-6 week postpartum mark, especially for aesthetic purposes, your muscles may begin to experience some relative atrophy and start relying on the support of the belly band to function normally, which in turn could make your core worse off than when you started.
Corsets and waist trainers are, in my opinion, unnecessary. Although some may love the aesthetic of an hourglass figure (because who doesn't) you are literally training your muscles and organs to shift PERMANENTLY. This is not a functional or healthy body type to maintain, especially for women who are recovering postpartum. Don't get me wrong, I'm all for shape wear (hello spanx!) but a tight hard-to-breathe garment to help slim your waist permanently seems a bit overboard. The best way to "slim down" and see a more defined waistline is learning how to correctly do a TVA breath, practicing proper posture, and eating a healthy balanced diet to maintain a healthy body fat %.