Image search is the second most frequently used search service on the Web. However, there are very few studies investigating any aspect of it. In this study, we investigate the precision of Web image search engines of Google and Bing for popular and less popular entities using text-based queries. Furthermore, we investigate four additional aspects of Web image search engines that have not been studied before. We used 60 different queries in total from three different domains for popular and less popular categories. We examined the relevancy of the top 100 images for each query. Our results indicate that image search is a solved problem for popular entities. They deliver 97% precision on the average for popular entities. However, precision values are much lower for less popular entities. For the top 100 results, average precision is 48% for Google and 33% for Bing. The most important problem seems to be the worst cases in which the precision can be less than 10%. The results show that significant improvement is needed to better identify relevant images for less popular entities. One of the main issues is the association problem. When a Web page has query words and multiple images, both Google and Bing are having difficulty determining the relevant images.