Provided are compositions and methods for detecting a target DNA (double stranded or single stranded) in a sample. In some embodiments, a subject method includes: (a) contacting the sample with: (i) a type V CRISPR/Cas effector protein (e.g., a Cas12 protein such as Cas12a, Cas12b, Cas12c, Cas12d, Cas12e); (ii) a guide RNA (comprising a region that binds to the type V CRISPR/Cas effector protein, and a guide sequence that hybridizes with the target DNA); and (iii) a detector DNA that is single stranded (i.e., a “single stranded detector DNA”) and does not hybridize with the guide sequence of the guide RNA; and (b) measuring a detectable signal produced by cleavage (by the type V CRISPR/Cas effector protein) of the single stranded detector DNA. Also provided are compositions and methods for cleaving single stranded DNAs (e.g., non-target ssDNAs), e.g., inside of a cell.