It is one of the key ways they say they are going to pay for their spending promises. Should we believe them?
First of all, tax avoidance and evasion are very different things.
Tax avoidance is legal and includes things that some people would consider to be normal tax planning.
Some parties refer to "aggressive tax avoidance". That is also legal but may involve the use of lawyers and accountants to find ways of avoiding tax that were not intended when tax regulations were introduced.
Tax evasion is illegal. It seems odd for political parties to say they are going to clamp down on tax evasion. It is like saying you are going to clamp down on theft and then putting a figure on how much you are going to save by doing so. On the plus side, it is unlikely that voters will say it is the wrong thing to do.
The Conservatives say they will save £5bn by clamping down on avoidance and evasion, the Liberal Democrats say £6bn and Labour tops the claims at £7.5bn.
Paul Johnson, from the Institute for Fiscal Studies, told BBC News: "All three parties are just making up numbers, quite honestly."
"Who knows whether that's feasible? Who knows whether that's the kind of money that's achievable? And frankly we'll never know."
And this is the key problem - it is very difficult to predict how much you can save by clamping down on avoidance and evasion, but Revenue & Customs (HMRC) also finds it very difficult to work out how much has been saved in the past.
It can tell you some of it. For example, it can tell you how much it has won at tax tribunals when there has been a legal dispute.
And it can try to put a figure on the outcome of specific policies, such as the tax cooperation agreement between the UK and Switzerland.
The Office for Budget Responsibility initially predicted that policy would raise £5.3bn.
But it later had to cut this figure to £1.9bn, which gives an idea of the margin of error in such forecasts.
When looking at a particular set of Budget anti-avoidance measures, the OBR concluded some had raised more than expected and some less, so the overall outcome had been pretty much as expected, which confirmed its warning that "avoidance costings are subject to significant uncertainty".
Why is it so difficult? Look at Labour's plans to abolish non-dom status, which was the subject of a previous Reality Check.
When you change the tax regulations, especially the way you tax the very rich, people tend to change their behaviour.
With non-doms, we do not know how much tax they would be paying if they did not enjoy this status. And it would be very difficult in retrospect to work out how much more tax had been raised as a result of its abolition.
To Labour's credit, it has not tried to put precise figures on the amount they would raise from the abolition, but it is part of their £7.5bn claim.
The Conservatives say they have raised £7bn by clamping down on avoidance, and point to this document to support their claim.
So maybe the figures are improving, although the publication is a bit short of detail.
On the other hand, this document from HMRC estimates that in 2012-13, £7.2bn was lost to the exchequer by avoidance and evasion.
Now, it may have risen considerably since then, but if £7bn has been saved already, it is hard to see where the extra billions are going to come from in the next Parliament.
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We've heard a lot in this election campaign about how much parties say they will save by clamping down on tax avoidance and evasion.