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Ionic liquids are promising candidates for novel electrolytes as they possess large electrochemical and thermodynamic stability and offer a high degree of tunability. As purely-ionic electrolyte without neutral solvent they exhibit characteristic structures near electrified interfaces and in the bulk, both being described theoretically via separate frameworks and methodologies. We present a holistic continuum theory applying to both regions. This transport theory for pure ionic liquids and ionic liquids-mixtures allows the systematic description of the electrolyte evolution. In particular, dynamic bulk-transport effects and interfacial structures can be studied. The theory is thermodynamically consistent and describes multi-component solutions (ionic liquids, highly concentrated electrolytes, water-in-salt electrolytes). Here, we give a detailed derivation of the theory and focus on bulk transport processes of ionic liquids as appearing in electrochemical cells. In addition, we validate our framework for a zinc-ion battery based on a mixture of ionic-liquid and water as electrolyte.