Text messages can be deleted individually or in bulk within the text conversation. Additionally, fully conversations can be deleted as well. 

To delete a message within a conversation:

1. Press and do a long hold on the text you would like to delete and click More... on the pop up.

2. Check the text message(s) you would like to delete and then select "Delete Messages".

*Please note that if you select all messages, you would in fact be deleting the entire conversation

To delete entire text conversations:

1. Swipe left to bring up the actions you can take on the conversation and tap Delete.

2. Press Delete Conversation to complete the action.