The aim of this talk is to introduce the subject of spin glasses,

and more generally the statistical mechanics of quenched disorder,

as a problem of general interest to physicists from multiple disciplines and

backgrounds. Despite years of study, the physics of quenched

disorder remains poorly understood, and represents a major gap in our

understanding of the condensed state of matter. While there are many

active areas of investigation in this field, I will narrow the focus of this

talk to our current level of understanding of the low-temperature

equilibrium structure of

realistic (i.e., finite-dimensional) spin glasses.

I will begin with a brief survey of why the subject is of interest not only

to physicists,

but also mathematicians, computer scientists, and scientists working in

other areas. A brief review of the basic features of spin glasses and what

is

known experimentally will follow. I will then turn to the problem of

understanding the nature of the spin glass phase --- if it exists.

The central question to be addressed is the nature of broken symmetry in

these systems. Parisi's replica symmetry breaking approach,

now mostly verified for mean field spin glasses, attracted great excitement

and interest as a novel and exotic form of symmetry breaking. But does it

hold also for real spin glasses in finite dimensions? This has been a

subject of intense controversy, and although the issues surrounding it have

become more sharply defined

in recent years, it remains an open question. I will explore this problem,

introducing new mathematical constructs such as the metastate along the way.

The talk will conclude with an examination of how and in which respects the

statistical mechanics of disordered systems might differ from that of

homogeneous systems.