  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.
