Cannot receive at all, or do not receive them from certain people?
A common problem with people who move from iPhone to Android is that they don't receive messages from their friends who still use iPhones. This is because the friend is still trying to use iMessage to send the messages rather than SMS (sometimes not realising that they are doing this), and iMessage only works between iOS devices (a deliberate choice by Apple not to make it available to other platforms). So if it's iPhone owners you are not getting messages from they may need them to look at their settings to make sure they use SMS for messaging to you rather than iMessage.
If the problem is more general, and you are sure the senders are using SMS rather than some messaging app that requires both of you to have it installed, then I'd suggest speaking to your carrier as this would sound like an account/network problem rather than a phone issue. But I suspect that my first guess is correct, because we've seen that a lot.