Emery and Clayton (2004) proposed that corvids (e.g. crows, ravens, jays) may have evolved – convergently with apes – flexible and domain general cognitive tool-kits. In a similar vein, others have suggested that coleoid cephalopods (octopus, cuttlefish, squid) may have developed complex cognition convergently with large-brained vertebrates but current evidence is not sufficient to fully evaluate these propositions. The aim of my thesis is to gain further insight into these issues. My first objective is to further our understanding of how deep the cognitive convergence between corvids and apes may be. To this end I report four empirical studies exploring cognitive complexity among different domains in a single species of corvids, the Eurasian jay (Garrulus glandarius). In Chapter 2, I investigate physical problem solving, finding that jays cannot spontaneously select functional tools according to their physical properties (i.e. size, shape) but can use novel tools – sticks – to solve a familiar task. In Chapter 3, I test whether future oriented caching in jays is underpinned by future planning abilities or by spontaneous predispositions; data do not support either hypotheses. In Chapters 4 and 5, I focus on social cognition. I find no indication that jays can integrate the visual perspective and current desire of competitors to protect their caches. Surprisingly, jays could also not respond to either of the two social cues independently, thus questioning the reliability of previously reported caching strategies. My second objective is to lay theoretical and methodological groundwork for studying convergent cognitive evolution between cephalopods and large-brained vertebrates. Therefore, in Chapter 6 I propose an evolutionary hypothesis for the emergence of large brains and behavioural flexibility in cephalopods and put forward novel paradigms that may allow researchers to explore the cognitive underpinning of octopus’ complex behaviours. I conclude by discussing the implication of my findings and future directions for the study of convergent cognitive evolution in corvids and cephalopods.