  We study influence of scalar fields on Nonlinear Electrodynamics spacetimes.
The investigation is carried out using both test and gravitating scalar fields.
After revisiting Einstein-Maxwell scalar field solutions we focus on analytic
investigation of Nonlinear Electrodynamics scalar field spacetimes, especially
Square Root Lagrangian model. The main motivation being to understand whether
certain specific signatures of scalar fields are preserved when Nonlinear
Electrodynamics as an additional source is considered. We show that the
regularity of horizon which is spoiled by scalar field in spherically symmetric
static scalar-vacuum spacetimes is not improved by including Nonlinear
Electrodynamics or other sources satisfying certain condition. We confirm these
findings using test scalar field that enables us to go beyond spherical
symmetry.
