I discuss the experimental evidence for and theoretical interpretation of the new mesons and baryons with two heavy quarks. These include doublyheavy baryons, exotic hadronic quarkonia and, most recently, a manifestly exotic pentaquark-like doubly heavy baryon discovered by LHCb with a minimal quark content uudc¯c. Its mass, decay mode and width are in agreement with a prediction based on a physical picture of a deuteron-like ΣcD¯∗ "hadronic molecule". In the second part of the paper, I focus on possible ways of experimental exploration of this new spectroscopy of QCD, especially in future high-energy e+e- colliders with very high luminosity. The primary task of these machines is searching for physics beyond the Standard Model. Consequently, their planned CM energy is far above the relevant energy scale for production of the new doubly-heavy hadrons. Yet, preliminary analysis of radiative-return processes indicates rather high effective luminosity at CM energies of interest, suggesting a possibility for copious production.