This paper provides an overview of recent research activities of the 5G AgiLe and fLexible integration of SaTellite And cellulaR (5G-ALLSTAR) project which aims to develop Multi-Connectivity technology that integrates the cellular and satellite networks to provide seamless, reliable and ubiquitous broadband services. 5G-ALLSTAR also entails developing millimeter-wave (mmWave) 5G New Radio (NR)-based cellular access system and investigating the feasibility of NR-based satellite access for providing broadband and reliable 5G services. In addition, spectrum sharing between cellular and satellite networks is studied. With all the technologies developed, 5G-ALLSTAR will showcase the first fully integrated satellite and cellular prototype system for 5G and beyond 5G (B5G) services at a big event (e.g., sporting event like Roland-Garros) in 2021. This paper also provides a preliminary techno-economic analysis on potential use cases targeting vertical markets, and introduces recent standardization activities of relevance.