Robots increasingly act as our social counterparts in domains such as healthcare and retail. For these human-robot interactions (HRI) to be effective, a question arises on whether we trust robots the same way we trust humans. We investigated whether the determinants competence and warmth, known to influence interpersonal trust development, influence trust development in HRI, and what role anthropomorphism plays in this interrelation. In two online studies with 2 × 2 between-subjects design, we investigated the role of robot competence (Study 1) and robot warmth (Study 2) in trust development in HRI. Each study explored the role of robot anthropomorphism in the respective interrelation. Videos showing an HRI were used for manipulations of robot competence (through varying gameplay competence) and robot anthropomorphism (through verbal and non-verbal design cues and the robot's presentation within the study introduction) in Study 1 (n = 155) as well as robot warmth (through varying compatibility of intentions with the human player) and robot anthropomorphism (same as Study 1) in Study 2 (n = 157). Results show a positive effect of robot competence (Study 1) and robot warmth (Study 2) on trust development in robots regarding anticipated trust and attributed trustworthiness. Subjective perceptions of competence (Study 1) and warmth (Study 2) mediated the interrelations in question. Considering applied manipulations, robot anthropomorphism neither moderated interrelations of robot competence and trust (Study 1) nor robot warmth and trust (Study 2). Considering subjective perceptions, perceived anthropomorphism moderated the effect of perceived competence (Study 1) and perceived warmth (Study 2) on trust on an attributional level. Overall results support the importance of robot competence and warmth for trust development in HRI and imply transferability regarding determinants of trust development in interpersonal interaction to HRI. Results indicate a possible role of perceived anthropomorphism in these interrelations and support a combined consideration of these variables in future studies. Insights deepen the understanding of key variables and their interaction in trust dynamics in HRI and suggest possibly relevant design factors to enable appropriate trust levels and a resulting desirable HRI. Methodological and conceptual limitations underline benefits of a rather robot-specific approach for future research.