  These proceedings discuss the current progress of the no-compromise approach
to the dimensional renormalization of chiral gauge theories in the context of
the BMHV scheme with non-anticommuting $\gamma_5$. Despite spuriously breaking
BRST-invariance in intermediate steps, it is the only scheme which handles the
well-known $\gamma_5$-problem mathematically consistently. We begin with a
brief motivation, followed by an exposition of our methodology. Specifically,
we illustrate the symmetry restoration procedure to obtain the required
symmetry-restoring counterterms and provide insights into our computational
setups, including recent developments. Building up on this, we present recent
results and advances for the multi-loop renormalization of Abelian and
non-Abelian chiral gauge theories, before concluding this article with a
discussion on prospective implementations of the BMHV regularization in SM-like
models.
