Regexes: the Bad, the Better, and the Best

Are regex slow?
In 2007 Russ Cox wrote his famous Regular Expression Matching Can Be Simple And Fast but not much has changed since then in the implementations of the most popular languages.
What can we do then?
The author presents three regexes that match the same input, analyzes the differences between them, and explains why the worst case is 20 times slower than the best one.