  The study of symmetric configurations $v_3$ with block size 3 has a long and
rich history. In this paper we consider two colouring problems which arise
naturally in the study of these structures. The first of these is weak
colouring, in which no block is monochromatic; the second is strong colouring,
in which every block is multichromatic. The former has been studied before in
relation to blocking sets. Results are proved on the possible sizes of blocking
sets and we begin the investigation of strong colourings. We also show that the
known $21_3$ and $22_3$ configurations without a blocking set are unique and
make a complete enumeration of all non-isomorphic $20_3$ configurations. We
discuss the concept of connectivity in relation to symmetric configurations and
complete the determination of the spectrum of 2-connected symmetric
configurations without a blocking set. A number of open problems are presented.
