Complex epilepsies are those requiring multidisciplinary management through a care pathway or for comorbidity (i.e. another pathology associated to the epilepsy, such as an intellectual deficit, behavioural disorders, metabolic diseases etc.). They can be of known or unknown aetiology.
Several groups of pathologies can be at the origin of a new-onset epilepsy, such as: Structural (brain lesions) that can be congenital (abnormal development of the cerebral cortex) or acquired (anoxic-ischaemic; head trauma); Genetic (that can be inherited or not); Metabolic; Infectious; or due to an Immune disease.  In an important number of cases the aetiology can be unknown, despite the realization of all currently available investigations.
Another example of complex epilepsies are the surgically treatable ones, requiring an early pre-surgical evaluation, a high level of multidisciplinary expertise and diagnostic resources (including video-EEG analysis, functional and/or structural neuroimaging).
Rare epilepsies include all the so-called developmental and epileptic encephalopathies, usually the result of a known or not yet characterized, genetic cause or other rare aetiology.
Finally, are considered complex epilepsies all those that resist to available antiseizure medications, particularly after a well-conducted trial of 2-3 drugs.
You can find here a list of the rare and complex epilepsies covered by the medical teams, members of EpiCARE.