This work examines three different concepts of objective redundancy in multiobjective optimization. Multiobjective optimization is known to suffer from the curse of dimensionality and we aim at reducing the number of objective functions which need to be considered. In this context, a set of objectives is called redundant if the sets of weakly efficient, efficient, or properly efficient solutions remain the same after removing the selected set of objectives. We clarify the relations between these three concepts and discuss combinatorial aspects with regard to the simultaneous and successive removal of objectives. We also provide sufficient conditions for each of these concepts. Further, we briefly discuss the connections to a stronger concept of redundancy which is useful for descent-type methods for solving multiobjective optimization problems.