Sendgrid and laravel 5 mail send and receive

I'm currently building a new version of an older website of mine and I'm trying to make a function that allowes users of mine to receive and send emails via that application. So they are be able to log in and send e-mails to another e-mail adress. Also if I sent an email to my domain I want to be able to receive the mail and have a catchall option. I'm currently using Laravel 5.1 and SendGrid.

I really don't know how to receive e-mails. The sending works.

via Chebli Mohamed