Anurag Kumar obtained his B.Tech. degree in Electrical Engineering from the Indian Institute of Technology at Kanpur in 1977, and was awarded the President of India's Gold Medal. He then obtained the PhD degree from Cornell University (1981), where he worked under the guidance of Prof. T.L. Fine. He was a Member of Technical Staff at AT&T Bell Labs, Holmdel, N.J., for over 6 years. During this period he worked on the performance analysis of computer systems, communication networks, and manufacturing systems. Since 1988 he has been with the Indian Institute of Science (IISc), Bangalore, in the Dept. of Electrical Communication Engineering (ECE), where he is now a Professor, and is also currently the Chairman of the Electrical Sciences Division. From 2000 to 2004 he was the Associate Chairman of the ECE Department, and from 2004 to 2007 he was the Chairman of the ECE Department. From 1989 to 2003 he was also the Coordinator at IISc of the nationwide Education and Research Network (ERNET) Project, which established the first country-wide packet communication network in India.

He was co-chair of the International Teletraffic Congress (ITC) sponsored seminar on Teletraffic Analysis Methods, Bangalore, 1993; program chair of the Conference on Signal Processing, Communications, and Networking (SPCOM), Bangalore, 1997; program chair of the IEEE Bangalore Section sponsored International Conference on Communications, Control and Signal Processing (CCSP2000), Bangalore, 2000; General co-Chair for the IEEE Workshop on Information Theory, Bangalore, October 2002; General chair of MCDES-2008 the IISc Centenary Conference of the Electrical Sciences Division of IISc.

He has served as an Area Editor for IEEE Transactions on Networking, and for IEEE Communications Surveys and Tutorials.

He has been elected a Fellow of the IEEE, a Fellow of the Indian National Science Academy (INSA), a Fellow of the Indian Academy of Science (IASc), and a Fellow of the Indian National Academy of Engineering (INAE). He has been awarded DST's J.C. Bose National Fellowship for the period 2011-2016.