In January 2015, an impressive outburst of the BL Lac object S5 0716+714 was registered in all energy bands, from low-frequency radio to very-high-energy gamma-rays (VHE, E > 100 GeV).
For the first time for this object, simultaneous $Fermi$-LAT and MAGIC spectra were obtained, allowing a close investigation of the higher-energy peak of the spectral energy distribution (SED).
The VLBA analysis of the parsec-scale jet, together with two-zone modeling of the simultaneous broadband SED, lead us to propose a scenario in which VHE emission arises during the entrance and exit of a superluminal knot through a recollimation shock in the inner jet. The gamma-ray emission in the high-energy (0.1 GeV < E < 100 GeV) and VHE bands is attributed to a shock-shock interaction in the helical jet downstream of the mm-wave VLBI core, closely followed by optical and X-ray outbursts that appear to occur in the core. An interpretation that the VHE gamma-ray emission is associated with a jet component entering and exiting the core region is consistent with the timing of the two VHE gamma-ray emission peaks, optical polarization angle (EVPA) behavior, and jet kinematics: the first peak took place $\sim$2 days after a very fast EVPA rotation, and the second $\sim$18 days after the new knot emerged from the 43 GHz VLBI core.
In December 2017 the source was detected by MAGIC at a flux level $\sim$6 times higher than that of the 2015 outburst.
We present the modeling of the 2015 flare and more recent results from the 2017 event.