In a world where e-commerce and social engagement are increasingly widespread among potential customers, search engines and social networks constitute powerful vehicles for companies’ advertising campaigns. Typically, an advertiser is required to indicate a bid for one or multiple keywords associated with a target ad. Then, a sponsored auction, conducted by the advertising platform and involving multiple advertisers, determines the visibility of each ad, which in turn influences the cost paid by the advertisers for the generated engagement. Designing optimal online bidding strategies, subject to time and budget constraints, can drastically improve companies’ profits. We review scientific papers on this topic from the last two decades, discuss the state-of-the-art frameworks used to approach the underlying optimization problems, and identify key research gaps and opportunities for future investigation.