  This paper gives an overview of the various approaches towards F_1-geometry.
In a first part, we review all known theories in literature so far, which are:
Deitmar's F_1-schemes, To\"en and Vaqui\'e's F_1-schemes, Haran's F-schemes,
Durov's generalized schemes, Soul\'e's varieties over F_1 as well as his and
Connes-Consani's variations of this theory, Connes and Consani's F_1-schemes,
the author's torified varieties and Borger's Lambda-schemes. In a second part,
we will tie up these different theories by describing functors between the
different F_1-geometries, which partly rely on the work of others, partly
describe work in progress and partly gain new insights in the field. This leads
to a commutative diagram of F_1-geometries and functors between them that
connects all the reviewed theories. We conclude the paper by reviewing the
second author's constructions that lead to realization of Tits' idea about
Chevalley groups over F_1.
