Whilst the dislocation core structure was investigated in the early days of the dislocation theory, the importance of core effects for understanding the basic features of plastic behaviour was first recognized in the case of bcc metals. At this time the first extensive computer modelling studies of dislocation cores were initiated. In this paper we show how the atomistic studies of dislocations advanced since these early calculations and how the basic ideas, developed at this time, apply when analysing deformation properties of other materials. Since a description of atomic interactions is the precursor of any atomistic calculations we first briefly describe the present status in this area, in particular the recently developed N-body potentials. Next, we discuss the concept of generalised stacking faults and associated energy-displacement surfaces (gamma-surfaces). In this part we demonstrate how the symmetry considerations can be used to assess the existence of possible metastable planar faults which play a role in dislocation splitting. A general discussion of planar and non-planar dislocation cores then follows in which the dislocation splitting and core phenomena are combined into one notion. These general concepts are illustrated by results of recent studies of the dislocation cores in hcp metals and intermetallic compounds with L1(2) and DO22 structures. Using these results we discuss the physical reasons for the following phenomena: preference for the prism slip in some hcp metals, anomalous positive temperature dependence of the yield stress for prism slip in beryllium, similar anomalous yield behaviour observed in L1(2) intermetallic compounds, such as Ni3Al, existence of another class of L1(2) compounds with a strong temperature dependence of the yield stress at low temperatures, and brittleness of DO22 compounds.