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.