Most common types of audit services include:

External audit (statutory audit)
These are the most widely used audit services. Examination of the accuracy of the financial statements is entrusted to external and independent auditor, who cannot be connected to the company or have any interest in the outcome of audit (no conflict of interests). The annual financial statement is certainly the main resource of accountability of the company. Since the financial statement is prepared and approved by the board of the directors, the shareholders of the company would rely on the external way to verify the report. Therefore, they invite external auditors. Moreover, regulations of many countries prescribe to run statutory audit on annual basis;
Internal audit (operational audit)
This is a voluntary pocedure of the organisation, willing to examine the effectiveness of inner control, verify and monitor possible fraud, check financial data, examine operational process and other activities. Basically, any company may conduct it for its own sake;
Tax audit
Tax audits are performed by tax authorities within regular intervals in some jurisdictions or in other randomly chosen countries. The purpose of the tax audit is to check company’s tax liabilities and to analyse accuracy of the filed tax returns;
Forensic audit
This is a special investigational audit conducted by legal officers and is often used in courts and investigation processes in order to determine frauds, tax evasion cases, money laundering and other illiegal actions within the framework of the company or its responsible officers.
how accountancy audit works
Audit requirements
Please note that in some countries every company must submit audited report (Cyprus, Singapore, Hong-Kong, Ireland) periodically. In other countries companies may prepare the audited report, if they meet certain criteria. The requirement for audit normally falls into a general rule:

If the company reaches 2 out of the below 3 thresholds, a sworn auditor must check the financial annual statement, before it is filed to the authorities:

The company’s turnover exceeds certain amount;
The company’s balance sheet exceeds certain amount;
Number of employees of the company exceeds certain amount.

Any company may as well choose an audit check voluntarily. There are different reasons why some companies choose to be checked by licensed auditors, even though there are no such obligations:

Licensed audit report provides extended creditability to the business in the eyes of company’s clients, suppliers, partners and banks;
Your own control over financial operations is the most obvious reason to request a check from the qualified professionals.
Audit report
The result of auditor’s work is an audit report. The report is usually done in a standard manner using generally accepted auditing standards (GAAS). You may come accross different variations of the audit report accustomed in different countries. However, every audit report must contain the following information:

Auditor’s opinion on whether the annual financial statement of the company reflects true and fair financial position or not;
Auditor’s confirmation on whether there were/weren’t any scope limitations imposed by the client;
Auditor’s statement, whether the annual report was/wasn’t materially misstated;
List of responsibilities of the auditor;
Scope of the audit;
Auditor’s independent opinion on the company’s financial status.
Audit report is later presented to the governmental institution or, alternatively, to the third party, serving as solid confirmation that a qualified specialist has provided his expertise and examined the financial statement of the company.

Audit Aftermath
Let’s highlight it once again: the aim of the report is to reflect the true and fair fainancial status. Recomendations given by the auditor should be appreciated and considered by the shareholders as they vividly show the company's shortcomings, hence it opens new vista for company’s improvements and accomplishments.