This year we celebrate the centenaries of the births of B. H. Neumann and A. I. Mal'cev, two great pioneers in the study of ordered algebraic structures. This paper is a survey of our recent progress in this area, and amplifies the talks we gave in Bath at the Groups St. Andrews Conference there, and the first author gave at the Mal'cev Centenary Conference in Novosibirsk. A version of this paper in Russian will appear in honour of the Mal'cev Centenary and the 80th anniversary of A. I. Kokorin, another pioneer in the subject (Izvestia of Irkutsk Sate University, Series Matematika, Vol. 2 (2009), No. 2, 4-19). The heart of the paper for pure group theorists is Section 4.
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机译：今年，我们庆祝B. H. Neumann和A. I. Mal'cev，两种伟大的先驱者在订购的代数结构研究中庆祝百年人。本文是对我们最近在这一领域的进展情况的调查，并放大了我们在那里的圣安德鲁斯大会上留下了浴室的谈判，第一个作者在新西伯利亚的Mal'cev Centenary会议上发布了。俄罗斯纸张的一篇文章将以纪念Mal'cev Centenary和Ai Kokorin的80周年纪念，这是AI Kokorin的另一个先驱（Irkutsk Sate Universy），Matematika系列，Vol。2（2009），2号，4-19）。纯粹团体理论家的纸质的核心是第4节。
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