Bridge piers on large rivers are often protected from scouring using launchable stone, such as a riprap sloping structure. While such scour countermeasures are effective for pier protection, they significantly alter flow conditions in the bridge opening by overtopping flow and flow contraction, deflecting the formation of the scour hole downstream and exposing the downstream riverbed to additional scour. This paper provides a comprehensive and relevant review of bridge scour estimation methods for piers with a riprap sloping structure installed as a scour countermeasure. Research on empirical methods for bridge scour estimation is reviewed and analyzed with formulae used for comparable structures—complex pier formulae and formulae for river training structures. A summary of relevant formulae applicable to piers with installed scour countermeasures is provided, as well as a discussion on the possible future research directions that could contribute to the field.