Three-dimensional (3D) topological Weyl semimetals (WSMs) represent the first observed manifestation of the elusive Weyl fermions, massless chiral particles predicted from a solution of Dirac equation by Hermann Weyl. In WSM those quasiparticles disperse linearly along all the three momentum directions across the corresponding Weyl points, which appear always in pairs of opposite chirality and act as source (or sink) for the Berry curvature. Since a finite Berry curvature at the Fermi level acts on fermions analogous to a magnetic field, the presence of sizeable so-called anomalous transverse transport quantities, viz. the anomalous Hall effect (AHE) and the anomalous Nernst effect (ANE) has been predicted as a direct proof of the existence of Weyl nodes close to the Fermi level. In this work, we show the experimental fingerprints of Berry-curvature-induced anomalous transport in different WSM candidates, promoting in particular the Nernst effect as an ideal bulk probe for detecting the emerging Weyl physics.