The first question is what carrier are you on, and which phone do you have? There are a number of reasons that SMS messages might not get through, and some of them might have nothing to do with you.
If you are on a GSM carrier (like AT&T/T-Mobile) then it could be an issue with your APN settings. Just do a google search for "APN settings for <insert your carrier name>". Also, certain settings on your device can cause issues when sending SMS/MMS messages when you are connected to WiFi.
Did you (or the person you are texting) happen to recently switch from an iPhone? iMessage in iOS does some special voodoo to handle SMS messages through Apple's own server, which can cause messages sent to or from you by iOS users who you previously communicated with via iMessage to be "swallowed" by Apple. There is a page on Apple's website with information about how to turn this off for your mobile number.
Another possibility begs another question: Are you using Google Voice? That can cause issues with certain carriers, especially with MMS messages.
You may also have your SMS app set to send all messages as MMS, and the person at the other end may not be able to receive SMS, or have their device set not to allow MMS messages.
As for not being able to call, what happens when you try to call them? These may be two unrelated things, that are just both happening at the same time (ie: they sent you a text, then went out of the service area).
And, at the end of the day, it might be a problem at their end. I have also seen issues where the specific tower you are attached to can cause issues. Has this been an on-going issue, or has it only been happening today? This is a very difficult problem to diagnose without a lot more info, but I will try to offer what help I can.
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