We will consider a family of non-classical three-valued logics that have been proposed to model indicative conditionals—sentences of the if-then type that occur in natural language, and concern what could be true (as opposed to counterfactuals, which concern eventualities that are no longer possible). Among these are the systems introduced by B. De Finetti, W.S. Cooper, J. Cantwell and R.J. Farrell, as well as some variants that have not appeared in the literature but seem nevertheless to be natural objects of interest from a formal point of view. We determine which of these logics are algebraizable, providing for the corresponding algebraic counterparts equational presentations from which finite Hilbert-style calculi can be readily obtained. Even in the non-algebraizable cases, we indicate how algebraic techniques may be employed to obtain further semantical insight into the logics and axiomatizations. Finally, we will point to possible extensions of the present work, such as further analysis of the relevant classes of algebras via twist-structure representations.