The authors try to solve (at least partially) some of the long standing problems in relation algebras. In a simple relation algebra, every element satisfying a certain condition is an atom. The question is if also the converse statement is valid. The authors give the solution in the negative. B. Jónsson proposed to find all finite simple relation algebras without simple proper extension. The authors show how to construct them in a particular case. They answer positively the problem whether there is a countable simple relation algebra that cannot be embedded in a one-generated relation algebra and solve a similar problem for \(k\)-generated simple relation algebras.