In the UK we never really got medium rise apartment blocks right. Instead we have terraces, which don't give the same housing density. The neighborhood I now live in in Portugal is mostly 7-10 storey apartment buildings, which is enough density for plenty of shops, cafes, restaurants, schools, playgrounds, public transit etc. It houses an astonishing amount of people in reasonably generous conditions (e.g. balconies are the norm), quite the modern miracle in my UK eyes.