In the last few years, there have been significant advances in migraine management and prevention. Lasmiditan, ubrogepant, rimegepant and monoclonal antibodies (erenumab, fremanezumab, galcanezumab, and eptinezumab) are new drugs that were launched on the US pharmaceutical market; some of them also in Europe. This publication reviews the available worldwide references on the safety of these anti-migraine drugs with a focus on the possible drug–drug (DDI) or drug–food interactions. As is known, bioavailability of a drug and, hence, its pharmacological efficacy depend on its pharmacokinetics and pharmacodynamics, which may be altered by drug interactions. This paper discusses the interactions of gepants and lasmiditan with, i.a., serotonergic drugs, CYP3A4 inhibitors, and inducers or breast cancer resistant protein (BCRP) and P-glycoprotein (P-gp) inhibitors. In the case of monoclonal antibodies, the issue of pharmacodynamic interactions related to the modulation of the immune system functions was addressed. It also focuses on the effect of monoclonal antibodies on expression of class Fc gamma receptors (FcγR).