As researchers strive to narrow the gap between machine intelligence and human through the development of artificial intelligence technologies, it is imperative that we recognize the critical importance of trustworthiness in open-world, which has become ubiquitous in all aspects of daily life for everyone. However, several challenges may create a crisis of trust in current artificial intelligence systems that need to be bridged: 1) Insufficient explanation of predictive results; 2) Inadequate generalization for learning models; 3) Poor adaptability to uncertain environments. Consequently, we explore a neural program to bridge trustworthiness and open-world learning, extending from single-modal to multi-modal scenarios for readers. 1) To enhance design-level interpretability, we first customize trustworthy networks with specific physical meanings; 2) We then design environmental well-being task-interfaces via flexible learning regularizers for improving the generalization of trustworthy learning; 3) We propose to increase the robustness of trustworthy learning by integrating open-world recognition losses with agent mechanisms. Eventually, we enhance various trustworthy properties through the establishment of design-level explainability, environmental well-being task-interfaces and open-world recognition programs. These designed open-world protocols are applicable across a wide range of surroundings, under open-world multimedia recognition scenarios with significant performance improvements observed.