The long arm of the law refers to the far-reaching power of the justice system. It suggests that no matter how far a criminal runs, or how clever their disguise, the authorities will catch up with them eventually.
While we often use this phrase to describe the police, the long arm of the law actually encompasses the entire legal system — from investigators and global extradition treaties to the courts themselves. The idiom evolved from the older concept of a long arm, which refers to any far-reaching power. The phrase is like a warning: You can't outrun the legal system.