The high penetration of both Distributed Energy Resources (DER) and Demand Response (DR) in modern power systems requires a sequence of advanced strategies and technologies for maintaining system reliability and flexibility. Real-time electricity markets (RTM) are the non-discriminatory transaction platforms for providing necessary balancing services, where the market clearing (nodal or zonal prices depending on markets) is very close to real time operations of power systems. One of the primary functions of RTMs in modern power systems is establishing an efficient and effective mechanism for small DER and DR to participate in balancing market transactions, while handling their meteorological or intermittent characteristics, facilitating asset utilization, and stimulating their active responses. Consequently, RTMs are dedicated to maintaining the flexibility and reliability of power systems. This paper reviews advanced typical RTMs respectively in the North America, Australia and Europe, focusing on their market architectures and incentive policies for integrating DER and DR in electricity markets. In this paper, RTMs are classified into three groups: Group I applies nodal prices implemented by optimal power flow, which clears energy prices every 5min. Group II applies zonal prices, with the time resolution of 5-min. Group III is a general balancing market, which clears zonal prices intro-hourly. The various successful advanced RTM experiences have been summarized and discussed, which provides a technical overview of the present RTMs integrating DER and DR.