Schemes of residual profit allocation (RPA) tax multinationals by allocating their 'routine' profits to countries in which their activities take place and sharing their remaining 'residual' profit across countries on some formulaic basis. They have recently and rapidly come to prominence in policy discussions, yet almost nothing is known about their impact on revenue, investment and efficiency. This paper explores these issues, conceptually and empirically. It finds residual profits to be substantial, but concentrated in a relatively few MNEs, headquartered in few countries. The impact on tax revenue of reallocating excess profits under RPA, while adverse for investment hubs, appears beneficial for lower income countries even when the formula allocates by destination-based sales. The impact on investment incentives is ambiguous and specific both to countries and MNE groups; only if the rate of tax on routine profits is low does aggregate efficiency seem likely to increase.