  Although quintessence models have attractive cosmological features, they face
two major difficulties. First, it has not yet been possible to find one which
convincingly realizes the goal of explaining present-day cosmic acceleration
generically using only attractor solutions. Second, quintessence has proven
difficult to obtain within realistic microscopic theories, largely due to two
major obstructions. Both of these difficulties are summarized in this article,
together with a recent proposal for circumventing the second of them within a
brane-world context. It is shown that this proposal leads to a broader class of
dynamics for the quintessence field, in which its couplings slowly run (or:
walk) over cosmological time scales. The walking of the quintessence couplings
opens up new possibilities for solving the first problem: that of obtaining
acceptable transitions between attractor solutions.
