The equivalence of particles and antiparticles — with difference only in the opposite signs of their charges, which follows from CPT invariance — is valid only for free, non-chiral fermions. With the weak interaction turned on the equivalence of particles and antiparticles is violated. Within the standard model even free neutrinos are exceptions, as they can be produced only in chiral states. Thus in spite of a long history of antiparticles, interesting theoretical and experimental challenges remain in their complete understanding. Finally, I overview the related experiments at the Antimatter Factory of CERN.