The name of Poincar remains well known in low-dimensional topology, 100 years after his death, thanks to the recent solution of his famous conjecture about the 3-sphere. In this talk we will try to recreate the world of 3-manifolds in the time of Poincar´e and his immediate successors, with special attention to the contributions of Heegaard, Wirtinger, Tietze, Dehn and Alexander.