Yeah, measles are fucking dangerous. They enter through the lungs (or sometimes the eyes), infect cells there and get replicated. They then get scooped up by immune cells called macrophages (part of the generalized immune system, which can react instantly, but can only deal with the "easy" stuff).
Normally this destroys the virus and parts of the pathogen get then transported into the lymph nodes as samples to produce antibodies against (which are needed as targets for the adaptive immune system) . Instead measles jump out of the macrophages and infect the T-cells (one of those 7 types of T-cells are the memory cells, which are "veterans" of previous infections and get reactivated when the same virus pops up again, instantly providing the info which antibody is needed).
The memory cells get wrecked, and with that any immunities you had before AND the ability to produce antibodies for anything. you are immunosuppressed for about 2 years.
There was a study which linked a previous measles infection with about 90% of all illness-related child deaths in third world countries, and is suspected to have caused more deaths in the first world with the damage to the immune system than through measles themselves.
also, if you are very unlucky, you can slowly die years after the measles infection, being sick for about 3 years - it's called SSPE, and it has a 95% lethality rate, and the 5% normally have massive brain damage.
i studied molecular biology (and had to abort my studies about 2 semesters before getting my Bachelor), and the virology courses were fascinating and horrifying at the same time. antivaxxers are uninformed, stupid people, and deserve to experience the same suffering they cause in their children and in society in general.