As a therapeutic intervention, homeopathy is the target of increased scepticism because in the main, its remedies are diluted and succussed (potentized) out of material existence. This puts homeopathy seemingly at odds with the paradigm of conventional science, in particular, that atoms and molecules are the fundamental building blocks of all matter. Accordingly, homeopathy cannot work, so that any reported beneficial effects must, at best, be due to the placebo effect. The purpose of this article is to challenge that conclusion and to suggest that there may well be conventional science-based explanations of how homeopathy could be possible. Homeopathy's key principles are first described. Then the double-blind randomized controlled trial (RCT), the chief means by which homeopathic remedies and prescribing are tested, is shown to be based on a linear reductionism that is too blunt an instrument with which to test the efficacy of complex interventions such as homeopathy The memory of water hypothesis, as a mechanism for how potentized remedies might work, is reviewed, along with some evidence for its existence. A possible rationale for the water memory effect is proposed in terms of a dynamic 'ordering' of water's constantly switching network of intermolecular hydrogen bonds, induced by the manufacturing process of homeopathic remedies. This could lead to a long-range molecular 'coherence' between trillions of mobile water molecules. However, the water memory effect is an essentially pharmacological explanation of homeopathy's putative efficacy. It is pointed out that healing also entails an interaction between consenting beings. From this point of view, an explanation of any therapeutic procedure should include an attempt to describe the nature of the patient-practitioner interaction. From this perspective, a quantum theoretical treatment of the therapeutic process, involving a form of macro-entanglement between patient, practitioner and remedy (PPR), is advanced as another possible explanation of the homeopathy's efficacy. This shows that the reason double-blind RCTs deliver at best only equivocal results on homeopathy's efficacy is because it effectively breaks the PPR entangled state. A comparison is made between the entanglement-breaking effect of double-blind RCTs and the wave-function 'collapsing' effect of observation in orthodox quantum theory. The article concludes by suggesting that the memory of water and PPR entanglement are not competing but most likely complementary hypotheses, and that both are probably required in order to provide a complete description of the homeopathic process. While awaiting experimental evidence of these hypotheses, it is suggested that observations of clinical outcomes would be superior to RCTs for further testing homeopathy's efficacy.