We discuss the combined effects of temperature, pressure and natural osmolytes on liquid-liquid phase separation (LLPS) phenomena of proteins, focusing essentially on the effect of pressure up to the kbar-regime. LLPS phenomena have been recognized to play an important role in the membrane-less compartmentalization of cells through the formation of biomolecular condensates. Various spectroscopy and microscopy techniques were employed to reveal structural changes and mesoscopic phase states of the systems. Quite unexpectedly, the LLPS of the compact and intrinsically disordered proteins studied are much more sensitive to pressure than folded states of globular proteins against unfolding. For example, at low temperatures, the phase-separated droplets of γ-crystallin dissolve into a homogeneous solution at as low as ~0.1 kbar whereas proteins typically unfold above 3-8 kbar. This observation suggests, in general, that organisms thriving at high-pressure conditions in the deep sea, with pressures up to the 1 kbar level, have to cope with this pressure-sensitivity of biomolecular condensates to avoid detrimental impacts on their physiology. As the birth place of life on Earth could have been the deep sea, studies of pressure effects on LLPS as presented here are also relevant to the possible formation of protocells under prebiotic conditions. Interestingly, our experiments demonstrate that trimethylamine-N-oxide, an osmolyte upregulated in deep-sea fish, significantly enhances the stability of the condensed protein droplets, pointing to a previously unrecognized aspect of the adaptive advantage of increased concentrations of osmolytes in deep-sea organisms. A molecular-level picture, in particular on the role of hydrophobic interactions, hydration and void volume in controlling LLPS phenomena at high pressures and in the presence of osmolytes is presented.