The earliest random matrices, namely the ubiquitous two by two contingency table, and the sample-covariance matrix for Gaussian observations, known as the Wishart matrix, both appeared in the field of statistics in the early 20th century. Research in random matrices in physics took off in the early 1950s since the introduction of the Wigner matrix. Soon after researchers started to look at the probabilistic aspects of different random matrix models. In mathematics, there were deep and surprising connections discovered between Wigner matrices and non-commutative probability. In the last three decades, there has been an explosion of research in both the theory and applications of random matrices, enveloping many different scientific disciplines. We provide a brief description of the contribution of Indian probabilists and statisticians to the theory and applications of random matrices, tracing its humble beginnings to the early 21st century. Currently faculty and students in Indian institutions are actively engaged in research in different aspects of random matrices, along with a significant group of relatively young researchers across the world of Indian origin, whose first exposure to random matrices took place as students in Indian institutions. Our advance apologies for any inadvertent omissions. We also emphasize that we have restricted our survey to only the work of probabilists and statisticians and have omitted contributions of researchers from other scientific disciplines.