Recently, several types of distributed energy resources (DERs) have been developed to reduce the environmental impact and support the global demand for electrical energy. However, the continuous penetration of the DERs into modern power systems (MPSs) may cause several adverse impacts in terms of operation performance indices (PIs) and power quality issues, especially in low-voltage distribution systems (LVDSs). To cope with these serious impacts and achieve optimal control, the hosting capacity (HC) of DERs must be accurately estimated and optimally optimized. However, it requires an extensive communication infrastructure, which is hardly offered without clear financial benefits. In this regard, this article investigates the historical developments of HC definitions as well as the recent developments in terms of operational performance indices, and estimation methods for active distribution networks (ADNs) with the high-penetration level existence of the DERs, energy storage systems (ESSs), electric vehicle (EV) charging systems, sector coupling, hydrogen technologies, and multi-carrier energy systems (MESs) to deal with electrical, thermal, and cooling demands. In this regard, this review article is intended to exhibit an appropriate reference for comprehensive research trends in HC estimation and optimization based on ADNs. Additionally, it involves and covers most current research HC topics in detail compared to other published review articles. Moreover, the authors deliberate the recent approaches for evaluating and improving the HC, especially concerning data-driven methods, with the aid of various software for simulating real systems. Moreover, modern research trends and main factors of MPS operations are deliberated with current energy market developments. Also, prominent challenges, current status, and future aspects are discussed.