Episodic memory involves the conscious recollection of personally experienced events and when absent, results in profound losses to the typical human conscious experience. Over the last 2.5 decades, the debate surrounding whether episodic memory is unique to humans has seen a lot of controversy and accordingly has received significant research attention. Various behavioural paradigms have been developed to test episodic- like memory; a term designed to reflect the behavioural characteristics of episodic memory in the absence of evidence for consciously experienced recall. In this review, we first outline the most influential paradigms that have been developed to assess episodic-like memory across a variety of non-human taxa (including mammals, birds and cephalopods), namely the what–where–when memory, incidental encoding and unexpected question, and source memory paradigms. Then, we examine whether various key features of human episodic memory are conceptually represented in episodic-like memory across phylogenetically and neurologically diverse taxa, identifying similarities, differences and gaps in the literature. We conclude that the evidence is mixed, and as episodic memory encompasses a variety of cognitive structures and processes, research on episodic-like memory in non-humans should follow this multifaceted approach and assess evidence across various behavioural paradigms that each target different aspects of human episodic memory. This article is part of the theme issue ‘Elements of episodic memory: lessons from 40 years of research’.