Shape memory polymer (SMP) is capable of memorizing one or more temporary shapes and recovering successively to the permanent shape upon various external stimuli. Beside of the above mentioned one-way variants, also two-way shape memory polymers (SMPs) and shape memory (SM) systems exist which feature a reversible shape change on the basis of "on-off switching" of the external stimulus. The preparation, properties and modelling of shape memory epoxy resins (SMEP), SMEP foams and composites have been surveyed in this exhaustive review article. The underlying mechanisms and characteristics of SM were introduced. Emphasis was put to show new strategies on how to tailor the network architecture and morphology of EPs to improve their SM performance. To produce SMEPs novel preparation techniques, such as electrospinning, ink printing, solid-state foaming, were tried. The potential of SMEPs and related systems as multifunctional materials has been underlined. Added functionality may include, among others, self-healing, sensing, actuation, porosity control, recycling. Recent developments in the modelling of SMEPs were also highlighted. Based on the recent developments some open topics were deduced which are merit of investigations in future works.