Copyright is merely property and as such if someone wants to use your property they must have your permission. Where copyright has been breached two obvious remedies are available. Breach of copyright often leads to an injunction being sought to bring the breach to an end. Injunctions can be granted at very short notice by the Courts. Usually the copyright owner also sues for damages.
Damages can be quite difficult to quantify.
If your copyrighted material has been damaged in any way the Court can compensate. If sales have been reduced then an award of damages can make up for the loss of those sales. Normally an injunction and damages are raised together in the one writ. In general, for fifty years after the authors death. The most likely related problem for web firms is passing off .