Non-relativistic quantum mechanics asserts the existence of entangled quantum states, that is multi-particle states for which individual particles cannot be given well-defined states. Such entangled states are ubiquitous; they form a dense subset of the space of composite quantum states. An important problem is to understand which types of entanglement are the same and which are different. We address this problem for systems of n quantum bits (qubits) by studying the action of the local unitary group SU(2)^n on the space of quantum states CP^(2^n-1). This talk will give some physical background to motivate the problem, then discuss the orbits and orbit space for two and three qubits. A general result for n qubits will also be mentioned.