  Entanglement quantification aims to assess the value of quantum states for
quantum information processing tasks. A closely related problem is state
convertibility, asking whether two remote parties can convert a shared quantum
state into another one without exchanging quantum particles. Here, we explore
this connection for quantum entanglement and for general quantum resource
theories. For any quantum resource theory which contains resource-free pure
states, we show that there does not exist a finite set of resource monotones
which completely determines all state transformations. We discuss how these
limitations can be surpassed, if discontinuous or infinite sets of monotones
are considered, or by using quantum catalysis. We also discuss the structure of
theories which are described by a single resource monotone and show equivalence
with totally ordered resource theories. These are theories where a free
transformation exists for any pair of quantum states. We show that totally
ordered theories allow for free transformations between all pure states. For
single-qubit systems, we provide a full characterization of state
transformations for any totally ordered resource theory.
