This paper contains a comprehensive review of the current status of our understanding of accidental explosions. After a short historical introduction in which all explosions are characterized by type, the first section discusses the general characteristics of explosions in some detail. Here the usually defined properties of blast waves are introduced and the classical point source or ideal wave is used to discuss scaling laws and TNT or point source equivalence in some detail. Following this there is a general summary of non-ideal blast wave behavior which first discusses extant theoretical work on blast waves from non-ideal sources, i.e., sources which are extended in either space or time. Secondly, each different non-ideal source property effect is discussed in detail with examples. Thirdly, atmospheric and ground effects are discussed briefly. In the next section the mechanisms by which blast waves produce damage are discussed in detail. In particular the new P-I (for pressure-impulse) method of evaluation is described in some detail with examples, the importance of dynamic impulse in producing tumbling and sliding is discussed, our understanding of fragment damage mechanism is presented and the classic TNT equivalence evaluation based on overpressure is described. In the last main section of the report specific examples of accidental explosions are given by type. The types that are discussed are: simple pressure vessel failure; runaway chemical reaction or continued combustion; explosions in buildings; internal explosions; rupture followed by combustion; vapor cloud explosions; high explosives and propellants; physical explosions and nuclear reactor runaway. The length of the discussion for each case is dependent on the potential hazard and extent of our current understanding of that type of explosion. The conclusion section summarizes the findings of the above. The main conclusions and recommendations are that 1. Accidental explosions are important and they will continue to occur. 2. Certain accidental explosions are more reproducible than others but virtually all of them are non-ideal. 3. TNT Equivalency is not a good criterion for evaluating non-ideal explosions and should be replaced, once our understanding improves. 4. Scaling laws for accidental explosions will be relatively easy to develop once our understanding of non-ideal explosions improves. 5. A considerable amount of work, both theoretical and experimental, is needed in this area.