I'll talk about the following problem: given a text t and a pattern p , both compresed using the LZW/LZ78 method, detect an occurrence of p in t (and find the leftmost, if any). It turns out that this problem can be solved in linear time in the compressed sizes of p and t (which can be as small as the square root of their original lengths). I'll start with the uncomprossed pattern case (which appeared at SODA'11) and then sketch some ideas behind extending this to the fully compressed case (which will appear at STACS'12).