We study optimal bidding strategies for advertisers in sponsored search auctions. In general, these auctions are run as variants of second-price auctions but have been shown to be incentive incompatible. Thus, advertisers have to be strategic about bidding. Uncertainty in the decision-making environment, budget constraints, and the presence of a large portfolio of keywords makes the bid optimization problem nontrivial. We present an analytical model to compute the optimal bids for keywords in an advertiser's portfolio. To validate our approach, we estimate the parameters of the model using data from an advertiser's sponsored search campaign and use the bids proposed by the model in a field experiment. The results of the field implementation show that the proposed bidding technique is very effective in practice. We extend our model to account for interactions between keywords, in the form of positive spillovers from generic keywords into branded keywords. The spillovers are estimated using a dynamic linear model framework and are used to jointly optimize the bids of the keywords using an approximate dynamic programming approach. Accounting for the interaction between keywords leads to an additional improvement in the campaign performance.