With the embodied interaction paradigm, research on human emotions has rapidly increased. In parallel, the advent of artificial intelligence and automated technologies has spurred research on trust towards interactive systems. However, little research has directly investigated the effects of emotions on trust in the context of technology use. The present paper surveyed empirical studies using the PRISMA framework. After briefly introducing emotional effects on cognitive processes, twenty-nine studies were systematically analyzed. In many papers positive emotions or empathically congruent systems led to higher trust. Some studies indicated that emotions can be a mediator between different factors and trust, whereas other studies showed only partial effects depending on different users or situations. Note that some research showed null effects or even negative effects (backfire effects) because emotional systems can be perceived as sarcastic or uncanny. In addition to the pervasive mood congruent effect or emotional contagion, various psychological mechanisms and theories were identified, such as entitativity, cognitive appraisal, or affect infusion model. Considerations for future design and research are discussed with results. This survey paper is expected to deepen the theoretical aspects of emotional effects on trust towards diverse technologies (robots, agents, or other interactive systems) and provide practical design directions.