Genomic breeding programs have been paramount in improving the rates of genetic progress of productive efficiency traits in livestock. Such improvement has been accompanied by the intensification of production systems, use of a wider range of precision technologies in routine management practices, and high-throughput phenotyping. Simultaneously, a greater public awareness of animal welfare has influenced livestock producers to place more emphasis on welfare relative to production traits. Therefore, management practices and breeding technologies in livestock have been developed in recent years to enhance animal welfare. In particular, genomic selection can be used to improve livestock social behavior, resilience to disease and other stress factors, and ease habituation to production system changes. The main requirements for including novel behavioral and welfare traits in genomic breeding schemes are: (1) to identify traits that represent the biological mechanisms of the industry breeding goals; (2) the availability of individual phenotypic records measured on a large number of animals (ideally with genomic information); (3) the derived traits are heritable, biologically meaningful, repeatable, and (ideally) not highly correlated with other traits already included in the selection indexes; and (4) genomic information is available for a large number of individuals (or genetically close individuals) with phenotypic records. In this review, we (1) describe a potential route for development of novel welfare indicator traits (using ideal phenotypes) for both genetic and genomic selection schemes; (2) summarize key indicator variables of livestock behavior and welfare, including a detailed assessment of thermal stress in livestock; (3) describe the primary statistical and bioinformatic methods available for large-scale data analyses of animal welfare; and (4) identify major advancements, challenges, and opportunities to generate high-throughput and large-scale datasets to enable genetic and genomic selection for improved welfare in livestock. A wide variety of novel welfare indicator traits can be derived from information captured by modern technology such as sensors, automatic feeding systems, milking robots, activity monitors, video cameras, and