The low energy effective description of Weyl and Dirac semimetals as massless Dirac fermions has given rise to new interpretations of thermal and thermo-electric transport phenomena in these materials, associated with quantum field theory predictions. In particular, quantum anomalies - most prominently the chiral anomaly - have provided a novel theoretical frame for the understanding of new magneto transport features. More recently thermal transport has taken the lead in relation to the gravitational anomaly. In this talk we will describe novel response functions associated with the scale anomaly in Dirac and Weyl semimetals. I will try to provide the foundations and the results in a pedagogical way.