In this talk, I will overview our recent works on quantum transport in topological semimetals of transition metal monopnictides (NbAs and NbP), and transition metal dipnictides (NbAs2, TaAs2 and TaSb2). For the former two non-centrosymmetric Weyl semimetals, we will elucidate the physical origin of the unprecedented charge carrier mobility, which are rooted in the unique helicity protection mechanism of Weyl fermions. For the latter dipnictide compounds, we will mainly focus on the anomalous magnetoresistance. We will show that high-quality TaSb2, which is the best-known compensated semimetal with non-saturating extremely large magnetoresistance, undergoes two topological phase transitions to reach the nearly perfect e-h compensation of < 0.1% mismatch. A systematic study indicates that such topological Lifshitz transitions are general and originate in the unique electronic band structure of the MPn2 family, which form the characteristic e-h-e structure along the I-L-I’ direction with nontrivial Z2 indices of [0;(111)]. With collinear B and E, negative magnetoresistance has been universally observed in MPn2, which may be correlated to Dirac surface states appeared in pair with the opposite helical spin structures.