How has psychology categorised different types of love? How has psychological theory categorised the different types of love?
What taxonomies of love are most accepted or useful in psychology?

EDIT:
I went through Triangular theory of love. Are there any other theories like this out there?
Sternberg's Triangular theory is certainly well-known. The field you want to dig into more is called 'close relationships'. Here's an accessible treatment of other common theories:


  Summary of psychological theories of love https://www.psychologytoday.com/us/blog/in-love-and-war/201208/love-decoded


This gives a good theoretical overview using many different approaches:


  More abstract positioning of theories of relationships and attachment with relation to other fields http://www.wwnorton.com/college/psych/intimate-relationships/ch/03/summary.aspx


Here's another I learned about in grad school: 


  Bem - Exotic Becomes Erotic: Interpreting the Biological Correlates of Sexual Orientation
  http://doi.org/10.1023/A:1002050303320