I would recommend against business logic inside components, unless you have dedicated higher order components with focussed responsibilities - but even that is not ideal. See "Caveats with using HOCs for side-effects" here.
Reducers are not ideal either because your logic may involve asynchronous steps.
In flux/redux logic belongs in action creators or sagas. The above answer also compares intelligent action creators with sagas.
I have lately resorted to putting logic in mostly framework independent Manager and Strategy classes with async functions which dispatch actions to communicate the results to the Redux store.