Embodiments of a method and a system for recovering energy, materials or both from asphaltene-containing tailings are disclosed. The asphaltene-containing tailings can be generated, for example, from a process for recovering hydrocarbons from oil sand. Embodiments of the method can include a flotation separation and a hydrophobic agglomeration separation. Flotation can be used to separate the asphaltene-containing tailings into an asphaltene-rich froth and an asphaltene-depleted aqueous phase. The asphaltene-rich froth, or an asphaltene-rich slurry formed from the asphaltene-rich froth, then can be separated into a heavy mineral concentrate and a light tailings. Hydrophobic agglomeration can be used to recover an asphaltene concentrate from the light tailings. Another flotation separation can be included to remove sulfur-containing minerals from the heavy mineral concentrate. Oxygen-containing minerals also can be recovered from the heavy mineral concentrate. Water removed by the various separation steps can be recycled and its heat energy recovered.