  We study real and complex interpolation of abstract Ces\`aro, Copson and
Tandori spaces, including the description of Calder\'on-Lozanovski{\v \i}
construction for those spaces. The results may be regarded as generalizations
of interpolation for Ces\`aro spaces $Ces_p(I)$ in the case of real method, but
they are new even for $Ces_p(I)$ in the case of complex method. Some results
for more general interpolation functors are also presented. The investigations
show an interesting phenomenon that there is a big difference between
interpolation of Ces\`aro function spaces in the cases of finite and infinite
interval.
