In recent years, the rapid advancement of machine learning (ML) models, particularly transformer-based pre-trained models, has revolutionized Natural Language Processing (NLP) and Computer Vision (CV) fields. However, researchers have discovered that these models can inadvertently capture and reinforce social biases present in their training datasets, leading to potential social harms, such as uneven resource allocation and unfair representation of specific social groups. Addressing these biases and ensuring fairness in artificial intelligence (AI) systems has become a critical concern in the ML community. The recent introduction of pre-trained vision-and-language (VL) models in the emerging multimodal field demands attention to the potential social biases present in these models as well. Although VL models are susceptible to social bias, there is a limited understanding compared to the extensive discussions on bias in NLP and CV. This survey aims to provide researchers with a high-level insight into the similarities and differences of social bias studies in pre-trained models across NLP, CV, and VL. By examining these perspectives, the survey aims to offer valuable guidelines on how to approach and mitigate social bias in both unimodal and multimodal settings. The findings and recommendations presented here can benefit the ML community, fostering the development of fairer and non-biased AI models in various applications and research endeavors.