If there are too many irrelevant variables in a linear regression model, the estimate for the relevant ones would be negatively affected. Therefore it is important both in theory and practice how to find the model which includes only the most important variables. Traditional approach is information criteria. LASSO gets popular in the past decade.

Literature:

Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Royal. Statist. Soc B., Vol. 58, No. 1, pages 267-288)

Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 301-320.

Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American statistical association, 101(476), 1418-1429.