In Computational Communication Science (CCS) researchers grapple with intricate ethical challenges arising from the collection and analysis of complex data sets, often including sensitive or copyrighted data. Taking into consideration differences between the two main lines of philosophical reasoning in the realm of (research) ethics—deontology and consequentialism—we argue that ethical challenges faced in CCS are multidimensional and, hence, require multiple perspectives and approaches. Our general considerations are complemented by an empirical study that aims to assess the nature, prevalence, and discussion of ethical issues in CCS literature. Through a manual content analysis of 476 CCS publications, we shed light on ethical challenges as well as reflections thereof by CCS researchers. Notably, we find that only 5.88% of studies explicitly address general ethical considerations. Ethical review processes are also only mentioned in 6.51% of the considered studies, with the majority focusing on specific ethical procedures, such as obtaining informed consent, data anonymization measures, or debriefing. This suggests that, in the absence of consensus and field-specific standards, researchers in CCS prioritize context-specific ethical procedures, emphasizing the importance of flexibility in addressing ethical considerations.