Bullying is defined as repeated negative actions involving a power differential, and intention to harm. There is limited research on harmful intention as a definitional component. This study explored the role of the perpetrator's harmful intention and the target's perception of harmful intention. Some 209 students (M = 14.5 years; 66.5% female) and 447 parents (M = 46.4 years; 86.4% female) were randomly assigned in an online survey. Participants assessed the likelihood of bullying in five hypothetical scenarios (physical, verbal, rumor, exclusion, and cyber) across five intention conditions, that also involved repetition and a power differential. The five intention conditions were: 1) harm intended by perpetrator (I) and perceived as intended to harm by target (I) [II condition]; 2) harm not intended by perpetrator (N) but perceived as intended to harm by target (I) [NI condition]; 3) harm intended by perpetrator (I) but not perceived as intended to harm by target (N) [IN condition]; 4) harm not intended by perpetrator (N) and not perceived as intended to harm by target N [NN condition]; and 5) a control which did not state any actual or perceived harmful intention [C condition]. For students and parents, the perpetrator's harmful intention and the target's perception of harmful intention were important when considering whether a peer interaction constituted bullying. These findings confirm the applicability of the three‐part definition of bullying, and highlight the importance of assessing these two dimensions of harmful intention when determining whether a problematic peer interaction should be regarded as bullying. Aggr. Behav. 43:352–363, 2017. © 2016 Wiley Periodicals, Inc.