Paper #1: Allen, T.A. and Fortin, N.J. The evolution of episodic memory. PNAS, doi:10.1073/pnas.1301199110.
Figure 1. The deep phylogeny of the proto-episodic memory architecture.
To understand the evolution of episodic memory, the authors attempt to reconstruct the deep evolutionary history of episodic memory (Figure 1). To do this, a series of homologous structures are proposed that are shared by birds and mammals. These structures (hippocampus, parahippocampal region, and prefrontal cortex) are then proposed as the seat of proto-episodic memory. Proto-episodic memory, which is shared by birds and mammals, has been thought to be convergent. In this paper, however, this capability is shown to be conserved, and present in the bird-mammalian ancestor.
While proto-episodic memory is highly conserved, not every species has an equivalent capacity. Indeed, as the prefrontal cortex (e.g. isocortex) is enlarged in humans, capabilities related to this structure are enhanced. This is due to species-specific functional differences that have emerged from the same basic architecture (Figure 2). In light of this, an intriguing comparison is made between episodic memory and fear conditioning. Fear conditioning (or emotional memory) is thought to be highly conserved  and characterized by one-trial encoding with inefficient recall. What distinguishes episodic memory from other types of memory are:
* content of the memory trace (the what, where, and when of events),
* structure of the memory trace (complex organization of task and information recall)
Figure 2. Episodic memory architecture in mammals (A) and birds (B) as compared to the proto-architecture (fundamental circuit, C).
Figure 3. Several candidate proximal mechanisms are thought to be responsible for brain enlargement in hominids.
The authors of this paper propose aerobic physical activity (APA) as the driver of such proximal (e.g. not explicitly evolutionary) mechanisms. From studies examining the effect of exercise on the brain, we know that APA generates and protects new neurons, increases the volume of brain structures, and improves cognition in living human brains . In cross-species comparisons based on artificial selection experiments, APA regimens administered to primates and rodents initiates activity-induced neurogenesis, which appears to improve memory and spatial learning. APA regimens also result in the upregulation of neurotrophins such as BDNF, IGF-1, and VEGF (e.g. growth and angiogenesis factors) in mice and humans alike. Across evolutionary time, it is proposed that selection for endurance running  also acted to increase baseline neurotrophic and growth factor signaling, which in turn enables the metabolic background for isocortical expansion (Figure 4).
Figure 4. An excellent rendition of brain evolution (for several structures) across the Order Primates. COURTESY: Robert Dahnke of the Structural Brain Mapping Group, University of Jena, Germany.
 This old view may have simply been an artifact of the view that human behavior is somehow special or "distinct" from other animal species. For example, Machiavellian-type behavior has been well-characterized in apes and monkeys, and caching behavior is well-known in birds.
More information on mental time-travel can be found here: Suddendorf, T. Mental time travel: continuities and discontinuities. Trends in Cognitive Sciences, 17(4), 151-152 (2013).
 This statement is in reference to evolutionary conservation of the main structure (amygdaloid) involved in fear consolidition. Paper (i) that proposes the amygdaloid structure was present in ancestral tetrapods, while paper (ii) demonstrates (through meta-analysis) that the amygdala is key in regulating emotional forms of memory:
(i) Moreno, N. and Gonzalez, A. Evolution of the amygdaloid complex in vertebrates, with special reference to the anamnio-amniotic transition. Journal of Anatomy, 211(2), 151–163 (2007).
(ii) Sergerie, K., Chochol, C., and Armony, J.L. The role of the amygdala in emotional processing: a quantitative meta-analysis of functional neuroimaging studies. Neuroscience Biobehavioral Reviews, 32(4), 811-830 (2008).
 Dunbar, R.I.M. The social brain hypothesis. Evolutionary Anthropology, 6(5), 178-190 (1998) AND Dunbar, R.I.M. The Social Brain: mind, language, and society in evolutionary perspective. Annual Review of Anthropology, 32, 163-181 (2003).
Here is a video (courtesy of Neuroanthropology blog) that critiques the Social Brain hypothesis from a social neuroscience perspective.
 Voss, M.W., Nagamatsu, L.S., Liu-Ambrose, T., and Kramer, A.F. Exercise, brain, and cognition across the life span. Journal of Applied Physiology, 111(5), 1505-1513 (2011).
 Bramble, D.M. and Lieberman, D.E. Endurance running and the evolution of Homo. Nature, 432, 345-352 (2004).