What are the different types of Testing methodology or testing models ?

Waterfall model: 

The waterfall model adopts a 'top down' approach regardless of whether it is being used for software development or testing. The basic steps involved in this software testing methodology are:
Requirement analysis ,Test case design ,Test case implementation ,Testing, debugging and validating the code or product ,Deployment and maintenance 
In this methodology, you move on to the next step only after you have completed the present step. There is no scope for jumping backward or forward or performing two steps simultaneously. Also, this model follows a non-iterative approach. The main benefit of this methodology is its simplistic, systematic and orthodox approach. However, it has many shortcomings since bugs and errors in the code are not discovered until and unless the testing stage is reached. This can often lead to wastage of time, money and valuable resources.

V model : 

The V model gets its name from the fact that the graphical representation of the different test process activities involved in this methodology resembles the letter 'V'. The basic steps involved in this methodology are more or less the same as those in the waterfall model. However, this model follows both a 'top-down' as well as a 'bottom-up' approach (you can visualize them forming the letter 'V'). The benefit of this methodology is that in this case, both the development and testing activities go hand-in-hand. For example, as the development team goes about its requirement analysis activities, the testing team simultaneously begins with its acceptance testing activities. By following this approach, time delays are minimized and optimum utilization of resources is assured.

Spiral model : Spiral Model

As the name implies, the spiral model follows an approach in which there are a number of cycles (or spirals) of all the sequential steps of the waterfall model. Once the initial cycle is completed, a thorough analysis and review of the achieved product or output is performed. If it is not as per the specified requirements or expected standards, a second cycle follows, and so on. This 
methodology follows an iterative approach and is generally suited for very large projects having complex and constantly changing requirements.

RUP : Rational Unified Process (RUP)

The RUP methodology is also similar to the spiral model in the sense that the entire testing procedure is broken up into multiple cycles or processes. Each cycle consists of four phases namely; inception, elaboration, construction and transition. At the end of each cycle, the product or the output is reviewed and a further cycle (made up of the same four phases) follows if necessary. Today, you will find certain organizations and companies adopting a slightly modified version of the RUP, which goes by the name of Enterprise Unified Process (EUP).

Agile model : Agile Model

This methodology follows neither a purely sequential approach nor does it follow a purely iterative approach. It is a selective mix of both of these approaches in addition to quite a few new developmental methods. Fast and incremental development is one of the key principles of this methodology. The focus is on obtaining quick, practical and visible outputs and results, rather than merely following theoretical processes. Continuous customer interaction and participation is an integral part of the entire development process.

Agile methods break tasks into small increments with minimal planning, and do not directly involve long-term planning. Iterations are short time frames (time boxes) that typically last from one to four weeks. Each iteration involves a team working through a full software development cycle including planning, requirements analysis, design, coding, unit testing, and acceptance testing when a working product is demonstrated to stakeholders. This minimizes overall risk and allows the project to adapt to changes quickly. Stakeholders produce documentation as required. An iteration may not add enough functionality to warrant a market release, but the goal is to have an available release (with minimal bugs) at the end of each iteration. Multiple iterations may be required to release a product or new features.

RAD : Rapid Application Development (RAD)

The name says it all. In this case, the methodology adopts a rapid development approach by using the principle of component-based construction. After understanding the various requirements, a rapid prototype is prepared and is then compared with the expected set of output conditions and standards. Necessary changes and modifications are made after joint discussions with the customer or the development team (in the context of software testing). Though this approach does have its share of advantages, it can be unsuitable if the project is large, complex and happens to be of an extremely dynamic nature, wherein the requirements are constantly changing