(Looking at top row and middle-right square in example below)

In the top row, 3 and 7 are an option for each cell, but 1 is in only two of them. Is there a technique for narrowing this down? Another example of this is the 3 and 8 and then the 1 in the middle-right section.

Also, are there any recommended strategies I could try using here? I've been looking, but I can't notice any. I haven't done much with puzzles like this, so I haven't needed to try any "advanced" strategies, but I'm really struggling now.