The Revenue also randomly selects a proportion of tax returns every year.
In the first two years of self-assessment, some 15,000 returns were investigated.
The Revenue will write to you to let you know that your affairs are being investigated although it will not normally give the reason behind its decision to launch an enquiry.
Under the self-assessment regime, the Revenue must start any enquiry within 12 months of the last filing date of 31 January but there is no requirement for an investigation to conclude within a fixed period of time. Some enquiries can last more than two years.
Most investigations are handled by local tax office inspectors with specialist training and experience. They know what to look for and are well versed in the excuses trotted out by wayward taxpayers who have underpaid their tax.
Whatever happens, taxpayers' affairs will be dealt with confidentially and information will only be disclosed to people that the individual agrees it may be given to, such as a tax accountant or other adviser.
The Revenue can, however, ask former employers, customers, suppliers or colleagues for information relating to its investigation.
The taxman is not required to give reasons for the enquiries it makes but it can identify areas that it wants to delve into.
If the problem appears to be a simple one of omission, it can ask taxpayers to answer specific questions or provide documents that might answer the question.
If it is discovered that tax has been underpaid, the taxpayer will have to pay what is due plus any penalty or interest accrued.
In serious cases of fraud, the Special Compliance Office can be involved. This is the Revenue's elite unit responsible for the most high-profile investigations.
Celebrity is no bar to investigation. The SCO has the power to negotiate settlements and can also agree not to prosecute a taxpayer as long as full disclosure is made.
In cases where minor amounts of income have been undeclared or where small mistakes have been made on the return, normally the matter can be cleared up with a few phone calls and submission of relevant pay slips.
But where serious fraud (amounts of more than ￡50,000) is concerned, the Revenue can start to request information from banks, accountants and other parties if it is the tax inspector's "reasonable opinion" that this will help the investigation.
Individuals with complex tax affairs or with a business to run may well find it easier to hire a specialist tax adviser or accountant to guide them through the process and minimise the disruption to their activities.
Prosecutions and the penalties can be severe including jail sentences and stiff fines designed to recoup the unpaid tax and penalties.
It is also possible to buy insurance to pre-empt the costs of a tax investigation.