It is known that the Standard Model of particle physics is incomplete in its description of
nature at a fundamental level.
For example, the Standard Model can neither incorporate dark matter nor explain the matter
dominated nature of the Universe.
This thesis presents three analyses undertaken using data collected by the LHCb detector.
Each analysis searches for indications of physics beyond the Standard Model in different decays
of $B$ mesons, using different techniques.
Notably, two analyses look for indications of new physics using indirect methods, and one uses
a direct approach.

The first analysis shows evidence for the rare decay $\B^+\!\rightarrow D_s^+\phi$
with greater than $3\,\sigma$
significance; this also constitutes the first evidence for a fully-hadronic annihilation-type
decay of a $B^+$ meson.
A measurement of the branching fraction of the decay $\B^+\!\rightarrow D_s^+\phi$ is seen to
be higher
than, but still compatible with, Standard Model predictions.
The $C\!P$-asymmetry of the decay is also measured, and its value is precisely in line with
the Standard Model expectations.

The second analysis claims the first observations of the decays
%$B^+\!\rightarrow K^+\pi^+\pi^-\mu^+\mu^-$ and $\B^+\!\rightarrow\phi K^+\mu^+\mu^-$
\btokpipimumu and $\B^+\!\rightarrow\phi K^+\mu^+\mu^-$
which are both flavour changing neutral currents, forbidden at leading order in the Standard
Model.
Branching fractions of both these decays are measured, and for the high statistics channel
$B^+\!\rightarrow K^+\pi^+\pi^-\mu^+\mu^-$ the differential branching fraction, as a function
of the invariant mass squared of the dimuon system, is also presented.

These first two analyses both constitute indirect searches for physics beyond the scope of the
Standard Model, where the observables are sensitive to contributions from new physics entering
at loop-level.
In contrast, the third analysis presented in this thesis involves the direct search for a new
dark boson, $\chi$, which is a messenger particle between a dark sector and the Standard Model
particles.
Using a frequentist technique, the dimuon component of candidates consistent with the decay
$B^{0}\!\rightarrow K^*(892)^0\mu^+\mu^-$ is searched for an excess indicative of
$\chi\!\rightarrow\mu^+\mu^-$.