  In this paper we give a survey of methods used to calculate values of
resistance distance (also known as effective resistance) in graphs. Resistance
distance has played a prominent role not only in circuit theory and chemistry,
but also in combinatorial matrix theory and spectral graph theory. Moreover
resistance distance has applications ranging from quantifying biological
structures, distributed control systems, network analysis, and power grid
systems. In this paper we discuss both exact techniques and approximate
techniques and for each method discussed we provide an illustrative example of
the technique. We also present some open questions and conjectures.
