What is compatibility testing?
In computer world, compatibility is to check whether your software is capable of running on different hardware, operating systems, applications , network environments or mobile devices.
Compatibility testing, part of software non-functional tests, is testing conducted on the application to evaluate the application’s compatibility with the computing environment.
Types of compatibility tests
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Hardware : It checks software to be compatible with different hardware configurations .
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Operating Systems: It checks your software to be compatible with different Operating Systems like Windows , Unix , Mac OS etc.
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Software: It checks your developed software to be compatible with other software’s.For example: MS Word application should be compatible with other softwares like MS Outlook,MS Excel , VBA etc.
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Network: Evaluation of performance of system In network with varying parameters such as Bandwidth, Operating speed, Capacity. It also checks application in different networks with all parameters mentioned earlier.
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Browser: It checks compatibility of your website with different browsers like Firefox , Google Chrome , Internet Explorer etc.
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Devices : It checks compatibility of your software with different devices like USB port Devices, Printers and Scanners, Other media devices and Blue tooth.
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Mobile: Checking you software is compatible with mobile platforms like Android , iOS etc.
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Versions of the software: It is verifying you software application to be compatible with different versions of software.For instance checking your Microsoft Word to be compatible with Windows 7, Windows 7 SP1 , Windows 7 SP 2 , Windows 7 SP 3.
There are two types of version checking 
Backward compatibility Testing is to verify the behavior of the developed hardware/software with the older versions of the hardware/software.
Forward compatibility Testing is to verify the behavior of the developed hardware/software with the newer versions of the hardware/software.
Compatibility testing process
1. Initial phase of compatibility testing is to define the set of environments or platforms the application is expected to work on.
2. Tester should have enough knowledge on the platforms / software / hardware to understand the expected application behavior under different configurations.
3. Environment needs to be set-up for testing with different platforms, devices, networks to check whether your application runs well under different configurations.
4. Report the bugs .Fix the defects. Re-test to confirm defect fixing.