This paper studies a search problem where a consumer is initially aware of only a few products. At every point in time, the consumer then decides between searching among alternatives he is already aware of and discovering more products. I show that the optimal policy for this search and discovery problem is fully characterized by tractable reservation values. Moreover, I prove that a predetermined index fully specifies the purchase decision of a consumer following the optimal search policy. Finally, a comparison highlights differences to classical random and directed search.