a) you host your complex infrastructure on premise:
you deal with. power issues, internet redundancy issues, ddos issue, physical access issues, disaster related issues (wildfire,flood,ground subsidence, earthquake, riots, collision with building, duststorm killing hvac, plague of locusts) , offsite/backups/highavailability issues and you deal also with most of the same things that cloud does. eg: if you do b2b auth with some other companies and they use and microsoft auth goes down..
b) or you make it someone elses problem and hope you have a good enough service level guarantee.