  We investigate the role of a quasiperiodically driven electric field in a
one-dimensional disordered fermionic chain. In the clean non-interacting case,
we show the emergence of dynamical localization - a phenomenon previously known
to exist only for a perfect periodic drive. In contrast, in the presence of
disorder, where a periodic drive preserves Anderson localization, we show that
the quasiperiodic drive destroys it and leads to slow relaxation. Considering
the role of interactions, we uncover the phenomenon of quasiperiodic
driving-induced logarithmic relaxation, where a suitably tuned drive
(corresponding to dynamical localization in the clean, non-interacting limit)
slows down the dynamics even when the disorder is small enough for the system
to be in the ergodic phase. This is in sharp contrast to the fast relaxation
seen in the undriven model, as well as the absence of thermalization
(drive-induced MBL) exhibited by a periodically driven model.
