For those not in the know, apps like Snapchat and Poke allow you to send photos, captions and videos that self-delete after a set amount of time (usually only a few seconds). Tigertext is a similar service, but for text messages rather than images. These apps are reportedly being used widely by teens and others to do things like sext (the texting equivalent of phone sex), pass notes and even cheat on tests. But a cheating spouse may also be using them to send messages to a paramour on the sly under the false assumption that the evidence will disappear forever.
A suspecting partner can also buy monitoring software or hardware that can recover deleted pictures and other data from phones or SIM cards. Just like with other types of data, deleting doesn't necessarily mean a picture is unrecoverable. And the cheater is bound to leave his or her phone lying around at some point.