When silage is exposed to air on opening the silo, or after its removal from the silo, fermentation acids and other substrates are oxidized by aerobic bacteria, yeasts and moulds. The aerobic stability of silage is a key factor in ensuring that silage provides well-preserved nutrients to the animal with minimal amounts of mould spores and toxins. In this paper, key findings and recent developments are reviewed, and findings of recent research are integrated in terms of four themes: (i) the most significant biochemical and microbiological factors, (ii) physical and management factors, (iii) type of additive and (iv) silo sealing. The development of yeasts and moulds during plant growth, and during field wilting or storage, and the concentration of undissociated acetic acid in silage are important microbiological and biochemical factors affecting aerobic stability. Silage density and porosity are key physical factors that affect the rate of ingress of oxygen into the silage mass during the feed-out period. A target for potential silage aerobic stability is 7 d including time in the feed trough. To achieve this target, speed of harvest should be coordinated with packing tractor weight to achieve a minimum silage density by the time of feed-out of 210 kg DM m−3, maximum proportional porosity of 0·4 and a rate of silage removal, which matches or exceeds the depth of air penetration into the silo. The use of additives to increase aerobic stability is advisable when there is the risk of these objectives not being met. Novel microbial approaches to solving the problem of silage aerobic deterioration are needed.