  This paper is an expanded version of the author's lecture at the Integers
Conference 2011. We discuss the secondary terms in the Davenport-Heilbronn
theorems on cubic fields and 3-torsion in class groups of quadratic fields.
Such secondary terms had been conjectured by Datskovsky-Wright and Roberts, and
proofs of these or closely related secondary terms were obtained independently
by Bhargava, Shankar, and Tsimerman; Hough; Zhao; and Taniguchi and the author.
  In this paper we discuss the history of the problem and highlight the diverse
methods used to address it.
