Most circuses claim to treat their animals well, and train them without using harsh methods. This probably does apply to animals such as performing dogs and horses, but when it comes to wilder animals like tigers and elephants the reality is often quite different. For example, when one goes to see lions in a circus act, the trainer usually has a whip and pointed pole to keep the lions away if they seem agressive. The only way the lions will know to keep back when the whip or stick is raised is if they've been trained to be afraid of it. I don't think this is an acceptable way of getting a creature to do what you want.
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As circuses are constantly on the move, the animals are crammed into trailers and boxcars for hours on end. It's not quite as bad for animals like horses dogs as they can be let out and allowed to move around in fields once the circus' destination has been reached. However, primates, large felines and elephants, who are potentially dangerous to performers and passers-by, are never allowed to wander around ouside. In the wild these animals would travel many miles daily, running free whenever and wherever they want to. As a result, these captive animals tend to be overweight and unfit due to lack of exercise.
In my opinion, a circus is much more enjoyable when it only involves human performers, such as Cirque du Soleil, because it means I'm not worrying about the welfare of the animals. Animal-friendly circuses are a much better option and are becoming more popular nowadays, so perhaps circuses with animals won't be around much longer.
The photo of the baby elephant is featured here and I copied it from here.