Extreme conditions have often provided a chance to discover new materials, new phenomena, and thus new physics. In this talk, two technologies will be introduced to produce such extreme condition, e.g., high temperature and high pressure. The first is electrostatic levitation (ESL) that provides containerless and contactless environment. Using the ESL, we can study physical properties of solids and liquids at high temperature (up to about 4000 K) and at deep supercooling, since it removes heterogeneous nucleation sites and any contamination sources by lifting liquid drop. The second is dynamic diamond anvil cell (dDAC) that is able to modulate a given static pressure with high compression rate, ~ 103 GPa/s. This device has been developed to study intermediate strain rate between static (<10-2 /s) and dynamic pressure (> 104 /s), since dDAC can control freely de/compression rate. This capability has been highly desired in high pressure physics community, because there have been discrepancies between static and dynamic pressure study which should be resolved. Using the two techniques, we study thermophysical properties and structure of liquids (metals, alloys, solutions, pure water). The study reveals a relation of the local order (short and medium range order) of supercooled liquids and nucleation barrier which is a key to understand (nano) crystallization, formation of bulk metallic glasses, glass transition, material synthesis, and so on. First, I will present how short and medium range order of supercooled liquid metals and alloys affect the nucleation. Second, multiple pathways of nucleation phenomenon will be shown on extremely highly supersaturated KH2PO4 (KDP) solution, which differs from classical nucleation theory. This phenomenon underlies the formation of metastable KDP crystal from the supersaturated solutions, by measuring real-time in-situ micro-Raman and X-ray scattering experiment. Third, I will demonstrate how supercompressed liquid water transforms into metastable crystal phase. In addition, ice crystal shows a growth transition as a function of compression rate by using the dynamic diamond anvil cell technique. In conclusion, the similarity of local order between liquids and crystals determines the path of phase transformation.