Can you elaborate on the dissimilarity between L1 and L2 regularization and how it's implemented in regression analysis? Also, when would you prefer one over the other?

Interview question asked to Machine Learning Engineers interviewing at Meetup, Groupon, Walmart and others: Can you elaborate on the dissimilarity between L1 and L2 regularization and how it's implemented in regression analysis? Also, when would you prefer one over the other?.