The big hot potato here is the evolutionary hypothesis that men are more sexually jealous whereas women are more emotionally jealous.
Contrast Harris (2003) totally dissing it (but also giving a nice summary of it, which is why I'm quoting it first):
The specific innate modular theory of jealousy hypothesizes that natural selection shaped sexual jealousy as a mechanism to prevent cuckoldry, and emotional jealousy as a mechanism to prevent resource loss. Therefore, men should be primarily jealous over a mate's sexual infidelity and women over a mate's emotional infidelity. Five lines of evidence have been offered as support: self report responses, psychophysiological data, domestic violence (including spousal abuse and homicide), and morbid jealousy cases. This article reviews each line of evidence and finds only one hypothetical measure consistent with the hypothesis. This, however, is contradicted by a variety of other measures (including reported reactions to real infidelity). A meta-analysis of jealousy-inspired homicides, taking into account base rates for murder, found no evidence that jealousy disproportionately motivates men to kill. The findings are discussed from a social-cognitive theoretical perspective.
Harris (of course) has her preferred counter-theory (as the last quoted sentence suggests; more on that in a moment). The contrast I want to make on the evolutionary issue is with Frederick and Fales (2016):
One hypothesis derived from evolutionary perspectives is that men are more upset than women by sexual infidelity and women are more upset than men by emotional infidelity. The proposed explanation is that men, in contrast to women, face the risk of unwittingly investing in genetically unrelated offspring. Most studies, however, have relied on small college or community samples of heterosexual participants. We examined upset over sexual versus emotional jealousy among 63,894 gay, lesbian, bisexual, and heterosexual participants. Participants imagined which would upset them more: their partners having sex with someone else (but not falling in love with them) or their partners falling in love with someone else (but not having sex with them). Consistent with this evolutionary perspective, heterosexual men were more likely than heterosexual women to be upset by sexual infidelity (54 vs. 35 %) and less likely than heterosexual women to be upset by emotional infidelity (46 vs. 65 %). This gender difference emerged across age groups, income levels, history of being cheated on, history of being unfaithful, relationship type, and length. The gender difference, however, was limited to heterosexual participants. Bisexual men and women did not differ significantly from each other in upset over sexual infidelity (30 vs. 27 %), regardless of whether they were currently dating a man (35 vs. 29 %) or woman (28 vs. 20 %). Gay men and lesbian women also did not differ (32 vs. 34 %). The findings present strong evidence that a gender difference exists in a broad sample of U.S. adults, but only among heterosexuals.
And what's the (alternative) social-cognitive theoretical perspective? Based on Wikipedia's summary (since Harris' own is waaay too long):
The social-cognitive perspective proposes the transactional model of jealousy, which can be used to explain why there may be differences in the degree to which individuals experience sexual jealousy within genders, as well as between genders. This model examines how three variables – (1) arousability, (2) commitment and, (3) insecurity – moderate jealousy.
- Individual differences in sexual jealousy are determined by the difference in levels of physiological arousal: individuals who are easily aroused have more intense jealous reactions, than those with lower physiological arousal.
- Commitment refers to the degree of dedication a person has in the relationship: the more committed a person is to a relationship, the greater the threat of loss, which leads to greater feelings of jealousy
- Insecurity refers to the perceived level of commitment of the partner: if we perceive our partner to be uninvolved or disinterested in the relationship, we feel more insecure.
The degree to which these factors are experienced together determine the intensity of sexual jealousy felt by an individual.
Wikipedia's summary seems mostly based on Erber, R., & Erber, M. W. (2016). Intimate relationships: Issues, theories, and research. New York, NY: Routledge.
The latter book actually has a chapter (TLDR) and the cheat-sheet at the end lists more theories:
• Prototype model defines jealousy as a subtype of anger
• Cognitive appraisal approaches contend that jealousy is a bona fide
• Bringle’s (1991) transactional theory of jealousy proposes that it arises
from the interplay between the individual and the situation
• Cognitive motivational approaches emphasize attributions and how we
think about jealousy-provoking situations
• The SEM [self-evaluation maintenance] approach focuses on the interaction between rival characteristics
and the jealous person’s self-evaluation
• Attachment model of jealousy predicts the intensity and frequency of
jealous reactions based on attachment type