  Recent measurements of $b\to s\mu^+\mu^-$ processes at LHCb and BELLE have
revealed tensions at the $2-3\,\sigma$ level between the Standard Model (SM)
prediction and the experimental results in the channels $B\to K^*\mu^+\mu^-$
and $B_s\to\phi\mu^+\mu^-$, as well as in the lepton-flavor universality
violating observable $R_K={\rm Br}(B\to K\mu^+\mu^-)/{\rm Br}(B\to Ke^+e^-$).
Combined global fits to the available $b\to s\mu^+\mu^-$ data suggest that
these tensions might have their common origin in New Physics (NP) beyond the SM
because some NP scenarios turn out to be preferred over the SM by
$4-5\,\sigma$. The fact that all these anomalies are related to muons further
suggests a connection (and a common NP explanation) with the long-standing
anomaly in the anomalous magnetic moment of the muon, $a_\mu$. In this article,
we study the impact of a generic class of NP models featuring new heavy scalars
and fermions that couple to the SM fermions via Yukawa-like interactions. We
consider two different scenarios, introducing either one additional fermion and
two scalars or two additional fermions and one scalar, and examine all possible
representations of the new particles under the SM gauge group with dimension up
to the adjoint one. The models induce one-loop contributions to $b\to
s\mu^+\mu^-$ and $a_\mu$ which are capable of solving the respective anomalies
at the $2\sigma$ level, albeit a relatively large coupling of the new particles
to muons is required. In the case of $b\to s\mu^+\mu^-$, stringent constraints
from $B_s-\overline{B}_s$ mixing arise which can be relaxed if the new fermion
is a Majorana particle.
