Hot problems in astroparticle physics today

The goal of this paper is to point out and discuss several of the most important points still open in astroparticle physics today. Of course, this paper is not exhaustive because of essentially two reasons: the first due to my knowledge and the second to the reasonable length of the paper. However, I will try to remark those hot points which will be discussed in more details during the workshop. I will outline the following items: 1) Introduction, 2) Cosmology, 3) Clusters of galaxies as gamma-ray emitters, 4) Cosmic counterparts of gamma-ray sources, 5) Active galactic nuclei and galactic collapsed objects: unified schemes, 6) Relativistic jets, 7) Gamma ray bursts, 8) X-ray binaries, 9) Neutrinos, 10) Some ideas on future missions, 11) Conclusions.