A modern vehicle is a complex system of sensors, electronic control units, and actuators connected through different types of intra-vehicle networks to control and monitor the state of the vehicle. In addition, modern vehicles are becoming increasingly connected to the outside world through V2X technologies. However, these provide new attack surfaces that increase the cybersecurity risk to modern vehicles. To this end, there are two distinct and key challenges that need to be addressed to ensure safety and consumer trust. While modern vehicles must be equipped with the best countermeasures against cybersecurity threats, a reliable mechanism shall be also in place to detect the potential intrusions of the system while in operation, which is termed as intrusion detection. This paper provides a structured and comprehensive review of the state of the art of the intra-vehicle intrusion detection systems (IDSs) for passenger vehicles. We first provide an overview of intra-vehicle networks before reviewing contemporary research in intra-vehicle IDSs. The approach employed is to categorize the reviewed works based on their detection technique and to examine the used feature and feature selection methods, evaluation dataset, attack type, performance metrics, and benchmark models. This paper also presents outstanding research challenges and gaps in intra-vehicle IDS research.