In the future, if medical technology is significantly advanced and humans live indefinitely, or at least for human lifespans have increased by tens or hundreds of years, how will marriage/divorce/monogamy be affected? What are reasons why marriage, divorce, and monogamous relationships would become more common, less common, or about the same as now?
The naive view might be that if technology is so advanced, people will indefinitely remain young unless they decline / cannot afford / aren't allowed treatments to keep them young. Having a young active body may encourage more casual relationships and cause people not to be married. However, I would argue that the usually more casual relationships of youth are related to chronological age / life experience, which obviously happen to be highly correlated with biological age, but is not caused as much by having a young body. So, even if people are biologically young, they may still get married because chronologically they've had some amount of life experience and feel like getting married.
If people live for hundreds of years, they will grow apart, so divorce will be a regular thing that happens after a few tens of years. So people will cycle through many marriages. Or knowing that this will happen, marriages will become much more contractualized and e.g. the marriage must last for X years before divorce is allowed.
Thinking of dating / marriage in terms of an sort of an optimal stopping problem or exploration/exploitation tradeoff, longer lifespans will allow for a much longer exploration phase, delaying the average chronological age at which people get married.
Two people who are biologically young could be vastly different chronological ages. The older one would have lived through many more historical events, had more life experiences, have more knowledge, etc. Think of grandpa with his wisdom marrying a 20 year old. In our current world, the main contribution of the 20 year in this marriage would probably be a young body, and also a youthful and energizing attitude. But if they are both people are biologically young, this is less of a relevant. So the chronologically older person may seek someone who is more compatible chronologically as well and has roughly the same amount of wisdom / experience etc. So this could cause stratification based on chronological age as well.
Depending on rules of wealth transfer between generations, marriage could take on more or less importance as a means of connecting people legally / financially / for immigration purposes, etc.
On the other hand, maybe marriage will still be very common but it will just increase the average chronological age at which people are married. Although two people may have the bodies of 25 year olds, they may chronologically be 50 years old, have had many explorative casual relationships, and now be very firm in their decision to remain married forever because they feel they've finally foudn someone very special that they will never want to leave.