First order differential equations

We consider a first order differential equation of  the form $f(y'; y) = 0$ with $f\in K[S; T]$ and $K$ a
differential field either complex or of positive characteristic.  We investigate several properties of $f$,
namely the 'Painlevé property' (PP), solvability and stratification. A modern proof of the classication
of first order equations with PP is presented for all characteristics. A version of the Grothendieck-Katz
conjecture for first order equations is proposed and proven for special cases. Finally the relation with
Malgrange's Galois groupoids and model theory is discussed.