Correction. The ionic liquids are solvents but not catalysts. The correct question would be "Are the ionic liquids the really green solvents ?

Ionic liquids are solvents.

Ionic Liquids (ILs) are categorize as solvent, however they may use as catalyst too,  for instance by immobilization of ILs on solid supports to prepare heterogeneous catalyst [DOI: 10.1039/B107946H]. 

Their physical properties make them unique solvents for synthesis, and are ‘green’ alternatives to volatile organic solvents; though there has been some debate on whether ionic liquids can be considered as ‘green’ solvents. [R. Sanghi & M.M. Srivasatava, Green Chemistry: Environment Friendly Alternatives, Alpha Science International, 2003, ISBN 9781842651735; C. Alfonso, A.M. Crespo & P.S.G. Joao, Green Separation Processes: Fundamentals and Applications, VCH-Wiley Publishing, 2005, ISBN 978357309856; J. Clark & J. Hardy, Green Chemistry in Undergraduate Practical Classes (with CD-ROM), Royal Society of Chemistry, 2006, ISBN 978054042784].

If you use ILs as a heterogeneous catalyst you can easily separate catalyst by filtration. 

I hope you will find this information useful.

Fouad

Compare to conventional organic solvents, ILs are greener solvent. However, it also act as catalyst. Please see these article 

http://pubs.acs.org/doi/abs/10.1021/jo201102q

http://pubs.rsc.org/en/Content/ArticleLanding/2011/CC/c1cc10151j#!divAbstract

http://pubs.acs.org/doi/abs/10.1021/ja900076a

It is very difficult to justify Ionic Liquid as complete green solvent.

I agree with Fouad Mohave that ionic liquids are not only act as solvents but also as catalyst. At present people condider the ILs as green solvents because of their unique physicochemical properties. In spite of these fascinating properties progress about their toxicity andecological impact is still inadequate.  Without having any sound knowledge about their  biodegradability and toxicological behavior,there may be no justification for calling them green. It has been observed that many commonly used ILs have a certain level of toxicity.In one of my article I have  reviewed & discussed about their effect on human’s health and environment. Have a look on this article certainly you will get answer.International Journal of Greenhouse Gas Control 20 (2014) 87–116

In my opinion, and that of a number of researchers, IL are not green solvents, even if they are less harmful than other organic solvents.

Nowadays in Ionic Liquids society these liquids are considered not green solvents.  Non-volatile behavior only could not be the basis greenness. However, using ionic liquids one can build up green processes if solving the IL recycling problems.

I believe that ILs can not be called green solvents in totality (if compared with water/no solvent system). No solvent is best solvent. However if the reactions mediated by ILs are proceeding dramatically different or if other conventional solvents are not suitable for reaction, the IL can be best option. It is not their non-volatility but their ability of getting tuned (by choosing/synthesising correct IL) to the properties conducive for reaction has made them important.

After completion of reaction the reaction mixture can be stirred with other suitable solvent (immiscible with ionc liquid) like ethyl acetate. The product of reaction enters into the added solvent. The solvent can be decanted and product can be collected by vacuum evaporation.  

ILs are not green solvents in general.

Ionic Liquids are categorize as solvent, however they may use as catalyst too

Correction. The term "Green" is used to show that these solvents follow the green chemistry rule. (And it does not means that it is extracted from plants.)

Green Chemistry is the design of chemical products and processes that reduce or

eliminate the use and generation of hazardous substances, and is based on Twelve Principles. 

1. Prevention 2. Atom Economy 3. Less Hazardous Chemical Syntheses. and so on...

A green solvent is a solvent that makes your process as green as it can be.  If the separation of product from the IL is difficult then probably the IL is not a green solvent for your process.  You also have to consider the manufacturing of the IL.  If the manufacturing of the IL made much more pollution than the manufacturing of another solvent that works for your process, then the IL is not a green solvent for you.  The most common ILs take 25 to 35 chemical steps to make, while conventional solvents take from 0 to 9 chemical steps to make.  Therefore most common ILs are not very green.

There really isn't  such a thing s a green solvent with the possible exception of water. What can be green though, or to be precise "greener" is your process (compared to another one), if by using certain chemicals and techniques  (which might, or might not include ionic liquids) you manage to use less chemicals, reduce carbon and other gas emissions, use less resources, recycle more, use less energy and produce less waste.

http://pubs.acs.org/doi/abs/10.1021/bk-2002-0818.ch003

The ionic liquids are not green solvents because of their toxic nature.

Madhukar Baburao Deshmukh

Why did you ask the question if you knew that

"The ionic liquids are not green solvents because of their toxic nature." This was known long time ago

… 

Can be or cannot be Green， it depands how the ils was synthesized and under what circumstances is it used and recycled.

Metaphysically speaking, CO2/water system can also be defined as ionic liquid in some conditions. They have the greenity in a degree.

I don't think so because of their toxic nature.

I tend to disagree, that ionic liquids are toxic as such. There are more possible ionic liquids than there are people on this planet. And just as people, they are different. There are toxic ones, there are also completely harmless ones, just as well there are some that are corrosive and others, which serve as corrosion inhibitors.

And that is the beauty of it, you can always find one, that can suit the properties profile that you are looking for.

You cannot state this generally.

When something is not "green", it is written that it is "green" because that's what money is for. Ionic liquids are considered "green", but this is just dream.

Depends on what you understand with „green“. There are a lot of parameters discussed nowadays such as life cycle assesment, carbon footprint, tox,..