We explore the origins of slow dynamics, aging and glassy rheology in soft and living matter. Non-diffusive slow dynamics and aging in materials characterised by crowding of the constituents can be explained in terms of structural rearrangement or remodelling events that occur within the jammed state. In this context, we introduce the jamming phase diagram proposed by Liu and Nagel to understand the ergodic-nonergodic transition in these systems, and discuss recent theoretical attempts to explain the unusual, faster-than-exponential dynamical structure factors observed in jammed soft materials. We next focus on the anomalous rheology (flow and deformation behaviour) ubiquitous in soft matter characterised by metastability and structural disorder, and refer to the Soft Glassy Rheology (SGR) model that quantifies the mechanical response of these systems and predicts aging under suitable conditions. As part of a survey of experimental work related to these issues, we present x-ray photon correlation spectroscopy (XPCS) results of the aging of laponite clay suspensions following rejuvenation. We conclude by exploring the scientific literature for recent theoretical advances in the understanding of these models and for experimental investigations aimed at testing their predictions.
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