  In this survey we discuss derivatives of the Wright functions (of the first
and the second kind) with respect to parameters. Differentiation of these
functions leads to infinite power series with coefficient being quotients of
the digamma (psi) and gamma functions. Only in few cases it is possible to
obtain the sums of these series in a closed form. Functional form of the power
series resembles those derived for the Mittag-Leffler functions. If the Wright
functions are treated as the generalized Bessel functions, differentiation
operations can be expressed in terms of the Bessel functions and their
derivatives with respect to the order. It is demonstrated that in many cases it
is possible to derive the explicit form of the Mittag-Leffler functions by
performing simple operations with the Laplace transforms of the Wright
functions. The Laplace transform pairs of the both kinds of the Wright
functions are discussed for particular values of the parameters. Some transform
pairs serve to obtain functional limits by applying the shifted Dirac delta
function.
