In this paper, omniconjugation is introduced as a topological phenomenon in pi-conjugated systems. Omniconjugated molecules are defined by the fact that they provide direct and fully pi-conjugated pathways between all subdstituents attached to them. Surprisingly, until now such topologies have never been explicitly recognized or investigated from this point of view. A topological design scheme is presented as a tool, which enables for the systematic construction of this novel class of pi-electron molecular structures. Molecular building blocks with three or more connection points to the external moieties are proposed, which for the first time allows for the interconnection of many functional entities in a fully conjugated manner. Omniconjugated structures may play an important role in the design of complex electronic circuitry based on organic molecules. On a larger scale, they may also giver rise to special material properties. Although omniconjugation is based on a valence-bond description of the system, it is shown that our concept is in good agreement with results obtained from a molecular-orbital description of the electron probability distribution in the frontier orbitals.