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Steady and oscillatory rheology was utilized to study the mechanical response of colloidal glasses and gels with particular emphasis in their yielding behaviour. We used a suspension of hard sphere colloidal particles with short-range depletion attractions induced by the addition of non-adsorbing linear polymer. While high volume fraction hard sphere glasses exhibit a single yield point due to cage breaking, attraction dominated glasses show a two-step yielding reflecting bond and cage breaking, respectively. Here we investigated the yielding behaviour of frustrated colloid–polymer systems with equal attraction strength and range, varying the particle volume fraction, φ, spanning the region from an attractive glass (φ = 0.6) to a low volume fraction (φ = 0.1) attractive gel. Yielding throughout this range, probed both by oscillatory and steady shear, is found to remain a two step process until very low φ's. The first yield strain related with in-cage or inter-cluster bond braking remains constant for φ > 0.3 while the second yield strain, attributed to braking of cages or clusters into smaller constituents, increases as volume fraction is decreased due to enhancement of structural inhomogeneities in the gel. Steady shear tests indicated distinct shear rate regimes: At steady state, low and intermediate shear rates create denser or smaller flowing clusters, whereas high rates may lead to complete break-up into independent particles. When the range of attraction was increased, both yield strains increased scaling with the range of attraction and accompanied structural changes. Finally, ageing leads to an overall strengthening of both the gel and the attractive glass accompanied by an enhancement of the second stress overshoot in steady shear, while the attractive glass also becomes more brittle.