Galileons theories have recently attracted a lot of attention. They can
be defined on flat space time as scalar theories which have field
equations exactly of second order. They have been generalized in various
ways, leading in particular in 4 dimensions to the so-called Horndeski
theories.
I will introduce these some of these generalizations and discuss two of
their aspects: first the counting of degrees of freedom in Horneski and
beyond Horndeski theories and secondly, aspects of p-form generalized
Galileons.