The phrasal verb look into means to find out about something and establish the facts in relation to it. If you look into something, you investigate it or examine it carefully. You might look into an issue in order to try to resolve it or look into a problem to see what is causing it.

1. After receiving numerous complaints about late deliveries, I promised my customers that I would look into what is causing the delays. 
2. When I lost my phone, my friend said that I should look into getting a free replacement from my network provider.

1. The police have confirmed they will look into who is vandalising our shop fronts.
2. We are not completely sure what the labour laws are around hiring interns, so our HR manager is going to look into it for us.