This thesis reports on an investigation of two non-trivial nucleation phenomena, with the goal that understanding these will enable greater understanding of nucleation generally.Non-photochemical laser-induced nucleation (NPLIN) phenomena have been investigated for more than twenty years but lack a complete explanation. The laser-induced phase separation and nucleation (LIPSaN) phenomenon has been discovered and it is proposed as the mechanism behind NPLIN. A laser generates a potential which, when incident on a binary mixture in proximity to its critical point, causes the high-refractive index component to migrate to the focus. The effect bears a similarity to optical trapping of particles, as the trapped particle has a higher refractive index than the medium it is in. It has been shown that nucleation can be induced in metastable binary mixtures, which is analogous to the metastable supersaturated solutions which are typical in NPLIN experiments. It is proposed that NPLIN can only work if there is a hidden liquid-liquid critical point in the supersaturated regime.The liquid-liquid transition (LLT) is a ubiquitous example of polyamorphism – the transition between one liquid state with no long-range ordering to another. There are several examples of LLTs, but none that are quite as fiercely debated as triphenyl phosphite (TPP). The debate can be summarised as two competing hypotheses: Hédoux – the second liquid does not exist; it is actually the untransformed liquid mixed with nano or micro scale crystals, or Tanaka – the second liquid state exists, but nano or micro crystals are also produced at higher LLT temperatures. It will be shown using a wide range of techniques that Tanaka is at least partially correct, but the two sides are two sides of the same coin. The second liquid state exists and there is a first order LLT, but the so-called nanocrystals are better described as locally favoured structures that are similar to the structure of the crystal. There are three crystal polymorphs of TPP and their distinct unit cells and conformers have been characterised with single crystal X-ray diffraction (XRD). There is a conformational change during the LLT which has been characterised using infrared, density functional theory (DFT) and XRD data. The LLT is associated by a flip of a phenoxy arm and change from parallel ‘sandwich’ to T-shaped π- π stacking. Both avenues of investigation emphasise the importance of critical points and their influence in how nucleation proceeds. The work presented here sheds some light on two poorly understood nucleation phenomena and will hopefully aid in a more robust understanding of nucleation generally.