The use of SNP-based measures of genome similarity to provide estimates of trait heritability has been developed over the past five years and has had a big impact on understanding the genetic architecture underlying the traits, and in predicting phenotype, for example in genomic selection.  I will review these advances and highlight some new developments, in gene-based tests of association and in meta-analysis.  The latter is joint work with Doug Speed of UCL Genetics Institute in London.