EU H2020 project “ASTERICS” (2014-2019) establishes a collaborative cluster to develop systems, tools and techniques for four next generation ESFRI telescope facilities in astronomy, astrophysics and astroparticle physics. In focusing on ELT, SKA, KM3NeT and CTA, ASTERICS achieved its aims. As outlined in this paper and described in detail in the papers of this publication, it solved key challenges common to the ESFRIs and adopted cross-cutting solutions with mutual and wide-ranging benefit to all concerned. ASTERICS facilitated the process of identifying areas ready for rapid technology development, where the adoption of a complementary and synergetic approach across the ESFRI projects could lead to significant added value in their operational phase.