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.
This month, a Sri-Lankan circus elephant, Anne, was moved to Longleat safari park in Wiltshire, after her owners were prosecuted with not seeing to her needs and repeatedly allowing for her to be beaten. These are offences under the 2006 Animal Welfare Act. The arthritic fifty-eight year-old pachyderm had been in the Bobby Roberts Super Circus since the 1950s. (I got this information from here.) Elephants are made learn tricks by being prodded with sharp rods and shocked with electric currents as babies.
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.