Simon Templar (Val Kilmer) is a theif. His next operation is to steal the formula for Cold Fusion, made by scientist Dr. Emma Russel (Elisabeth Shue).
So, Simon tries to get Emma to fall in love with him, so he can then steal the formula. He later falls in love with her, so he doesn't want to steal it anymore. So, the Russians get mad and threaten Simon.
Throughout the movie, he uses different disguises to steal and get what he wants. He used different accents also. He poses as a German guy, an older American man, a cop... all sorts of characters.