The failure of a rolling bearing may cause the shutdown of mechanical equipment and even induce catastrophic accidents, resulting in tremendous economic losses and a severely negative impact on society. Fault diagnosis of rolling bearings becomes an important topic with much attention from researchers and industrial pioneers. There are an increasing number of publications on this topic. However, there is a lack of a comprehensive survey of existing works from the perspectives of fault detection and fault type recognition in rolling bearings using vibration signals. Therefore, this paper reviews recent fault detection and fault type recognition methods using vibration signals. First, it provides an overview of fault diagnosis of rolling bearings and typical fault types. Then, existing fault diagnosis methods are categorized into fault detection methods and fault type recognition methods, which are separately revised and discussed. Finally, a summary of existing datasets, limitations/challenges of existing methods, and future directions are presented to provide more guidance for researchers who are interested in this field. Overall, this survey paper conducts a review and analysis of the methods used to diagnose rolling bearing faults and provide comprehensive guidance for researchers in this field.