Nowadays, with the advancement of technology, world is trending toward high mobility and dynamics. In this context, intersection management (IM) as one of the most crucial elements of the transportation sector demands high attention. Today, road entities including infrastructures, vulnerable road users (VRUs) such as motorcycles, moped, scooters, pedestrians, bicycles, and other types of vehicles such as trucks, buses, cars, emergency vehicles, and railway vehicles like trains or trams are able to communicate cooperatively using vehicle-to-everything (V2X) communications and provide traffic safety, efficiency, infotainment and ecological improvements. In this paper, we take into account different types of intersections in terms of signalized, semi-autonomous (hybrid) and autonomous intersections and conduct a comprehensive survey on various intersection management methods for heterogeneous connected vehicles (CVs). We consider heterogeneous classes of vehicles such as road and rail vehicles as well as VRUs including bicycles, scooters and motorcycles. All kinds of intersection goals, modeling, coordination architectures, scheduling policies are thoroughly discussed. Signalized and semi-autonomous intersections are assessed with respect to these parameters. We especially focus on autonomous intersection management (AIM) and categorize this section based on four major goals involving safety, efficiency, infotainment and environment. Each intersection goal provides an in-depth investigation on the corresponding literature from the aforementioned perspectives. Moreover, robustness and resiliency of IM are explored from diverse points of view encompassing sensors, information management and sharing, planning universal scheme, heterogeneous collaboration, vehicle classification, quality measurement, external factors, intersection types, localization faults, communication anomalies and channel optimization, synchronization, vehicle dynamics and model mismatch, model uncertainties, recovery, security and privacy.