The book gives an overview of developments in Quantitative Genetics and variance component analysis in an era of Big Data and Sequenced Genomes. It provides a detailed description of a direct method of estimation that will be a useful means of extracting information from a large set of data that was inconceivable 10 to 20 years ago. The book is a combination of a history of variance component analysis and a forward looking view as to how direct methods of estimation arise from the availability of big data sets and sequenced genomes of each individual in the sample. Many papers and books on quantitative genetics versions of the general linear model from statistics are useful for analyzing the data, using relatively small sets of data. In this book, new methods of direct estimation are introduced and analyzed that are appropriate for an era of big sets of data and sequences genomes. These direct methods of estimation are based on taking conditional expectations rather the methods of least squares that characterize many applications of the general linear model of statistics.