Searchable encryption is a very appealing concept to store data on an untrusted server, so as to keep search functionalities while ensuring privacy of both the queries and the data. Many different solutions emerged, differing on their security and on their efficiency, originating both from the industry and the academia. Actually, these past few years, searchable encryption has actually been a very hot topic, a lot of work on new constructions or new attacks has been done. In this presentation, I will try to give an insight on the big challenges of searchable encryption, and explain why the compromise between security and performance is the core problem in this area. To do so, I will talk about lower bounds, recent attacks and constructions, and ongoing work, both theoretical and practical. This will give you a glimpse at the variety of techniques and tools that can be applied to searchable encryption, and at how wide this topic can be, ranging from theoretical computer science, to systems design. Finally, I will conclude by describing some exciting open problems on searchable encryption, again both theoretical and practical.