How can I "grep" recursively filtering the name of the files I want with wildcards?

Use grep's --include option:

grep -ir "string" --include="*.php" .

If you have a version of grep that lacks the --include option, you can use the following. These were both tested on a directory structure like this:

$ tree
.
├── a
├── b
│   └── foo2.php
├── c
│   └── d
│       └── e
│           └── f
│               └── g
│                   └── h
│                       └── foo.php
├── foo1.php
└── foo.php

Where all the .php files contain the string string.

1. Use find

   $ find . -name '*php' -exec grep -H string {} +
   ./b/foo2.php:string
   ./foo1.php:string
   ./c/d/e/f/g/h/foo.php:string
   

   Explanation

   This will find all .php files and then run grep -H string on each of them. With find's -exec option, {} is replaced by each of the files found. The -H tells grep to print the file name as well as the matched line.

2. Assuming you have a new enough version of bash, use globstar :

   $ shopt -s globstar
   $ grep -H string  **/*php
   b/foo2.php:string
   c/d/e/f/g/h/foo.php:string
   foo1.php:string
   

   Explanation

   As explained in the bash manual:

   globstar

   If set, the pattern ‘**’ used in a filename expansion context will match all files and zero or more directories and subdirectories. If the pattern is followed by a ‘/’, only directories and subdirectories match.

   So, by running shopt -s globstar you are activating the feature and Bash's globstar option which makes **/*php expand to all .php files in the current directory (** matches 0 or more directories, so **/*php matches ./foo.php as well) which are then grepped for string.