This section gathers together material on two-surface twistors and Penrose's quasi-local momentum and angular momentum construction. The articles give an incomplete view of work on the construction in that, by and large, the many successes of the construction are not well represented here. It should be remembered that where it worked, which was chiefly with ‘non-contorted’ 2-surfaces (defined below), the construction worked well. What is on display here is the struggle to find a way to deal with ‘contorted’ 2-surfaces: different avenues were explored and different modifications were suggested and it is this ferment of activity that is best represented. It is also the case that, for some of the results that follow, the original Twistor Newsletter article has until now been the only complete reference.