Gamma-Ray Bursts (GRBs) are one of the main targets for current and next
generation Imaging Atmospheric Cherenkov Telescopes (IACTs). Given their
transient behavior, especially in the case of their prompt emission phase,
performing fast follow-up observations is challenging for IACTs, which have a
narrow field of view and limited duty cycle. Despite this, MAGIC plays a major
role in the search for Very High Energy (VHE, E>100 GeV) gamma-ray emission
from GRBs: this is possible thanks to its fast repositioning speed, low energy
threshold and high sensitivity at the lowest energies. In 2013 the MAGIC GRB
automatic procedure was upgraded, increasing the number of GRBs followed in the
prompt and early afterglow phases and decreasing dramatically hardware failures
during fast repositioning. Currently, only GRB 190114C was firmly detected in
the VHE band, while for other GRBs no significant detection was achieved. In
such a case, upper limits (ULs) can give insight into the physics driving such
eluding sources, especially on their emission mechanisms. In this contribution
we report on the status of the GRB follow-up with MAGIC and focus on the ULs
and results obtained from a sample of GRBs observed between 2013 and 2018. This
GRB catalog is the result of the MAGIC well-designed and tested follow-up
procedure, and it serves as a precursor of GRBs observation with the next
generation IACT system, the Cherenkov Telescope Array (CTA).
