How do I restrict an input to only accept numbers?

Easy way, use type="number" if it works for your use case:

<input type="number" ng-model="myText" name="inputName">

Another easy way: ng-pattern can also be used to define a regex that will limit what is allowed in the field. See also the "cookbook" page about forms.

Hackish? way, $watch the ng-model in your controller:

<input type="text"  ng-model="myText" name="inputName">

Controller:

$scope.$watch('myText', function() {
   // put numbersOnly() logic here, e.g.:
   if ($scope.myText  ... regex to look for ... ) {
      // strip out the non-numbers
   }
})

Best way, use a $parser in a directive. I'm not going to repeat the already good answer provided by @pkozlowski.opensource, so here's the link: https://stackoverflow.com/a/14425022/215945

All of the above solutions involve using ng-model, which make finding this unnecessary.

Using ng-change will cause problems. See AngularJS - reset of $scope.value doesn't change value in template (random behavior)

Using ng-pattern on the text field:

<input type="text"  ng-model="myText" name="inputName" ng-pattern="onlyNumbers">

Then include this on your controller

$scope.onlyNumbers = /^\d+$/;

Here's my implementation of the $parser solution that @Mark Rajcok recommends as the best method. It's essentially @pkozlowski.opensource's excellent $parser for text answer but rewritten to only allow numerics. All credit goes to him, this is just to save you the 5 minutes of reading that answer and then rewriting your own:

app.directive('numericOnly', function(){
    return {
        require: 'ngModel',
        link: function(scope, element, attrs, modelCtrl) {

            modelCtrl.$parsers.push(function (inputValue) {
                var transformedInput = inputValue ? inputValue.replace(/[^\d.-]/g,'') : null;

                if (transformedInput!=inputValue) {
                    modelCtrl.$setViewValue(transformedInput);
                    modelCtrl.$render();
                }

                return transformedInput;
            });
        }
    };
});

And you'd use it like this:

<input type="text" name="number" ng-model="num_things" numeric-only>

Interestingly, spaces never reach the parser unless surrounded by an alphanumeric, so you'd have to .trim() as needed. Also, this parser does NOT work on <input type="number">. For some reason, non-numerics never make it to the parser where they'd be removed, but they do make it into the input control itself.