The therapeutic efficacy of a drug or its unexpected unwanted side effects may depend on the concurrent use of a medicinal plant. In particular, constituents in the medicinal plant extracts may influence drug bioavailability, metabolism and half-life, leading to drug toxicity or failure to obtain a therapeutic response. This narrative review focuses on clinical studies improving knowledge on the ability of selected herbal medicines to influence the pharmacokinetics of co-administered drugs. Moreover, in vitro studies are useful to anticipate potential herbal medicine-drug interactions. In particular, they help to elucidate the cellular target (metabolic or transporter protein) and the mechanism (induction or inhibition) by which a single constituent of the herbal medicine acts. The authors highlight the difficulties in predicting herbal–drug interactions from in vitro data where high concentrations of extracts or their constituents are used and pharmacokinetics are missed. Moreover, the difficulty to compare results from human studies where different kinds of herbal extracts are used is discussed. The herbal medicines discussed are among the best sellers and they are reported in the “Herbal Medicines for Human Use” section of the European Medicinal Agency (EMA).