The reaction between hydrogen and oxygen is in principle the simplest method to form hydrogen peroxide, but it is still a “dream process”, thus needing a “dream catalyst”. The aim of this review is to analyze critically the different heterogeneous catalysts used for the direct synthesis of H2O2 trying to determine the features that the ideal or “dream catalyst” should possess. This analysis will refer specifically to the following points: (i) the choice of the metal; (ii) the metal promoters used to improve the activity and/or the selectivity; (iii) the role of different supports and their acidic properties; (iv) the addition of halide promoters to inhibit undesired side reactions; (v) the addition of other promoters; (vi) the effects of particle morphology; and (vii) the effects of different synthetic methods on catalyst morphology and performance.