A process for regenerating a used acidic ionic liquid catalyst, comprising: a. contacting the catalyst and hydrogen with a supported hydrogenation catalyst under hydrogenation conditions; and b. recovering a conjunct polymer that is a clear and colorless oil from the catalyst. A process for regenerating a used acidic ionic liquid catalyst which has been deactivated by conjunct polymers comprising the steps of contacting the used catalyst and hydrogen with a supported hydrogenation catalyst in a reaction zone under hydrogenation conditions in the presence of an inert hydrocarbon in which saturated conjunct polymers are soluble for a time sufficient to hydrogenate at least a portion of the conjunct polymers; and recovering the saturated conjunct polymers. Also, a process comprising: contacting the used acidic ionic liquid catalyst and hydrogen with a hydrogenation catalyst comprising a hydrogenation component under hydrogenation conditions; and recovering a conjunct polymer that is a clear and colorless oil.