There are many types of software testing that can and should be automated. Some of the most common types of automated testing include:

• Unit testing
• Integration testing
• System testing
• Acceptance testing

In addition to these common types of automated testing, there are also a number of other types of testing that can be automated, such as:

• Performance testing: Performance testing tests the performance of the software under different loads.
• Security testing: Security testing tests the security of the software against a variety of attacks.
• Usability testing: Usability testing tests the usability of the software for users.

The decision of whether or not to automate a particular type of testing depends on a number of factors, such as the cost of automation, the risk of defects, and the importance of the test. In general, it is more cost-effective to automate tests that are repetitive, time-consuming, or difficult to perform manually. Tests that are critical to the quality of the software should also be automated.

Further, if you want to know about various types of software testing, here is a blog to read.