On Borel subgroups in the Cremona groups

It has long noticed the analogy between affine algebraic groups and the Cremona groups. One of the main elements of the structural theory of affine algebraic groups are Borel subgroups. Their key feature is conjugation. The concept of a Borel subgroup makes sense for the Cremona groups as well. This naturally leads to attempts to understand their role in the theory of these groups, in particular, to explore the problem of their conjugation. The first results in this direction was obtained by H. Bass in 1984. Now we know more on this topic. I shall tell about the results, known to me, on this range of issues.