Generalized Baumslag-Solitar groups are a class of combinatorially interesting groups. Their group theory is also closely associated to a the topology of a class of 2-dimensional spaces. These 2-dimensional spaces are Seifert fibred. We develop the basic topology of these fibrations and derive some of the most immediate group theoretic consequences of this topology.

This survey article has two components. The first part gives a gentle introduction to Serres notion of $G$-complete reducibility, where $G$ is a connected reductive algebraic group defined over an algebraically closed field. The second part concerns consequences of this theory when $G$ is simple of exceptional type, specifically its role in elucidating the subgroup structure of $G$. The latter subject has a history going back about sixty years. We give an overview of what is known, up to the present day. We also take the opportunity to offer several corrections to the literature.

Groups St Andrews 2013 was held at the University of St Andrews from 3rd August to 11th August 2013. This was the ninth in the series of Groups St Andrews group theory conferences organised by Colin Campbell and Edmund Robertson of the University of St Andrews. There were just under 200 mathematicians from over 20 countries involved in the meeting as well as some family members and partners. The Scientific Organising Committee of Groups St Andrews 2013 (all from St Andrews) was Colin Campbell, Max Neunhöffer, Martyn Quick, Edmund Robertson and Colva Roney-Dougal.

This time the academic business of the conference ran for seven days from Sunday 4th August to Saturday 10th August. Four main speakers delivered four talks each, surveying areas of contemporary development in group theory and related areas; Emmanuel Breuillard (Université Paris Sud 11), Martin Liebeck (Imperial College), Alan Reid (University of Texas), and Karen Vogtmann (Cornell University). There were five invited speakers delivering one-hour plenary talks: Peter Cameron (St Andrews), Radha Kessar (City University, London), Markus Lohrey (Universität Leipzig), Derek Robinson (University of Illinois at Urbana-Champaign) and Christopher Voll (University of Bielefeld). In addition there were nearly 100 contributed short talks from the delegates.

In the evenings throughout the conference there was an extensive social programme. The main conference outing was to the Royal Burgh of Falkland either to visit Falkland Palace or, as it turned out, to go on an adventure walk in the Lomond Hills. Other highlights of the social programme were a whisky tasting evening, a musical evening and the conference banquet. Once again The Daily Group Theorist was a nice feature of the conference. We thank the various editors of this, by now traditional, publication.

The support of the two main United Kingdom mathematics societies, the Edinburgh Mathematical Society and the London Mathematical Society has, once again, been an important factor in the success of these conferences. As well as supporting some of the expenses of the main speakers, the grants from these societies were used to support postgraduate students and also participants from Scheme 5 and fSU countries.