This paper studies realization theory and canonicity conditions for implicit systems. Here an implicit system is any system defined by an input-output finite-dimensional, linear, time-invariant relation in discrete or continuous time. The familiar definitions of canonicity and minimality are extended to such systems. A reduced form is used to prove the equivalence of minimality and canonicity. The notion of transfer function is replaced by that of an external form and it is shown that a minimal realization can always be achieved.