A short review of up-to-date experimental data and theoretical notions concerning crystallization and the glass transition in complex hydrocarbon systems – crude oils and their fractions – is presented. Special attention is given to the behavior of crude oils and their fractions at high pressure. It is demonstrated that all oils may be approximately divided into two classes. For the first class of oils and fractions (with high initial viscosity), one can observe the onset of the non-equilibrium glassification process at decreasing temperature or increasing pressure. For those in the second class (with low viscosity), cooling or increased pressure leads to a multi-step crystallization process (mainly of n-alkanes) continuing up to the onset of main matrix glassification. For all oils and fractions investigated, crystallization does not influence the position of the glass transition line of the main matrix.