A couple of years ago I bought a pair of trail running shoes, thinking I was going to try running. It turns out that running is not my favorite activity so they did not get used much.
When I started working out at home again, doing P90x3 I just figured I could use those shoes with my workouts. Then during the workout Tony Horton would keep emphasizing on NOT WEARING RUNNING SHOES! So I did a little research on what shoes you should be wearing.
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These shoes are only for what they say they are for and that is running. Running shoes are not built for lateral moves that often come with doing variety of workouts like HIIT or home workouts. If you are a frequent runner this is the type of shoe you want to look for, since they tend to have more stability in the forefoot to support your landing.
Court shoes are built for supporting the side to side to side movements. They are ideal for your mixed workouts of lifting and cardio often found in home workout videos. They are generally flatter shoes with good all around support.
Walking shoes believe it or not are slightly different than running shoes. For a running shoe you want more support in your forefoot but for walking you want more support in your heal.
Cross Trainer Shoes
If you do a little of everything and only occasionally then a cross trainer shoe may be good for you. Unless you do a specific activity, like running, more than 3 days a week than a cross trainer shoe will work. Look for a sturdy heal, good support, and light weight.