The concept of affordances is used in robotics to model action opportunities of a robot on objects in the environment, and as such they play a role in building basic cognitive capabilities of the robot. Affordances generally model isolated objects in the environment and capture the interdependencies between object properties, executed actions on those objects, and the effects of those respective actions. However, many real-world scenarios involve configurations of multiple objects that interact with each other when manipulated. This thesis proposes the use of recent advances in statistical relational learning to build relational affordance models, where the (spatial) relations between the different objects, such as relative distances between pairs of objects, are taken into account. Two-object interaction models are learned from the robot interacting with the objects in the world in a behavioural babbling stage. These models can then be employed in situations with arbitrary numbers of objects. This model thus generalizes over objects and can deal effectively with uncertainty. To show the relevance of relational affordance models, we further investigate the use of relational affordances in three different applications. These applications are illustrated by the use of the iCub and PR2 robots in simulation, and the use of the iCub robot in a real setting. Firstly, we use SRL methods to create a relational affordance model for two-arm robot actions, for settings where these can be approximated by a combination of the two single-arm actions composing them. The arms may act simultaneously or sequentially, and the robot is given background knowledge about possible actions in its environment. SRL is used here to generalise and build a higher-level model for a set of two-arm actions settings in a household environment, by using symmetries of the arms to model effects of actions executed with the arm not involved in the behavioural babbling stage, and background knowledge about two-arm actions. Secondly, we employ relational affordance models in a planning setting with high-level goals which are specified by (spatial) relations between the objects. The relational affordance model can be used to define a state transition model in a table-top setting, and we provide a planning algorithm to be used to infer the next best possible action for the robot to execute towards reaching the given goal. The robot is then given a series of planning tasks of increasing difficulty in a table-top environment, which it needs to solve. Finally, to tackle an occluded object search task, we use the concept of relational affordances to search for any object affording a given action in a kitchen environment with many shelves. Multiple object types can afford the action, and eachtype allows for many different objects with size and shape modelled by probability distributions, thus relaxing some of the previous assumptions in the field. Moreover, we allow for stacked objects, a more realistic modelling of objects in shelves, introducing more complex object spatial relations.