  We discuss and illustrate the appearance of topological fermions and bosons
in triple-point metals, where a band crossing of three electronic bands occurs
close to the Fermi level. Topological bosons appear in the phonon spectrum of
certain triple-point metals, depending on the mass of atoms that form the
binary triple-point metal. We first provide a classification of possible
triple-point electronic topological phases possible in crystalline compounds
and discuss the consequences of these topological phases, seen in Fermi arcs,
topological Lifshitz transitions and transport anomalies. Then we show how the
topological phase of phonon modes can be extracted and proven for relevant
compounds. Finally, we show how the interplay of electronic and phononic
topologies in triple-point metals puts these \textit{metallic} materials into
the list of the most efficient \textit{metallic} thermoelectrics known to date.
