1. Introduction

2. Melting relations

3. The case of water, H₂O

4. Pressure-induced amorphisation and polyamorphism: general considerations

5. Liquid-liquid phase transitions and the “two-state” model to interpret melting curve maxima

6. The “two-state” model, liquid-liquid transitions, and extension to other systems

7. The relationship with glassy state polyamorphism, PIA, and the negative slope of the melting curve: the general nature of L-L phase transitions

8. Extensions of the two-state model, and its implications for rheology

9. Revisiting Y₂O₃-Al₂O₃: the effects of the compositional variable and the evolution towards “normal” liquid-liquid immiscibility

10. Summary