Australia is a sovereign country and has the right to decide who can enter and stay on its territory. Only Australian citizens have the unrestricted right to travel freely in and out of the country. All other people must have an authority, in the form of a visa, to enter and stay in Australia. With the exception of New Zealand citizens, travelling on New Zealand passports, all foreign nationals must obtain a visa or Electronic Travel Authority before travelling to Australia.
Anyone who arrives without a visa, authority for re-entry or an Australian or New Zealand passport will be refused entry to Australia or delayed until their identity and claims to enter Australia have been checked.
Australian citizens, who have automatic right of entry to Australia, need only present a current Australian passport on arrival. Australian citizens, who hold dual or multiple nationalities, must use an Australian passport to enter or leave Australia, even if they use a foreign passport overseas. The only exception is where they have been issued an Australian Declaratory Visa (ADV).
New Zealand citizens, travelling on New Zealand passports, receive electronic visas on arrival, entitling them to stay in Australia.
All other non-citizens, including people who migrated and now live in Australia permanently, must hold a valid visa or authority for re-entry to Australia. New migrants are issued with a multiple re-entry visa when their immigration to Australia is approved. These visas last up to five years from the date of grant. After the initial visa has expired, if the holder wishes to continue to travel to and from Australia as a permanent resident, they must obtain a Resident Return Visa (RRV).
A permanent resident (migrant) cannot travel on their migrant visa once they have been granted Australian citizenship. This is because the migrant visa ceases by law when Australian citizenship is acquired, even though it may not yet have reached its expiry date or been physically cancelled.
See also:
Fact Sheet 45 - Visas - Questions and Answers

        Visitor visas and Business visitor visas are available, in Electronic Travel Authority (ETA) form, from over 300,000 travel agents, more than 75 airlines, Australian diplomatic offices overseas and online if making travel bookings through the internet.
If you do not hold a passport approved for ETA, you will need to apply for a 'label' visa from Australian diplomatic offices overseas such as Australian Embassies, High Commission offices or Consulates.
To make a valid application for a visa for Australia, you must:

• indicate the type or class of visa which you want,
• use the correct form,
• pay the required charge,
• provide the correct documentation in support of your application,
• satisfy other requirements for that visa, and
• send or deliver your application to an Australian diplomatic office overseas.

You must also:

• complete the form in English,
• answer all questions truthfully - if you provide incorrect information or documents, your visa may later be cancelled, and
• provide certified copies of all documents. Please do not provide originals unless requested by the Department.

See also:
Information Form 1025i Making and processing visa applications. ( PDF File )

        Australia's Electronic Travel Authority system (ETA) is the most advanced and streamlined travel authorisation system in the world. It is the modern-day replacement for a visa label or a stamp in a passport, although these are still used where the ETA is not yet available.
ETA enables visitors from passport approved countries to obtain authority to enter Australia at the same time as they book their travel arrangements. There is no need for the traveller to complete an application form for a visa. The ETA is issued within seconds by computer links between the Department, over 300,000 travel agents, more than 75 airlines and specialist service providers around the world.
The ETA system can also be accessed online, enabling tourists and business travellers intending to visit Australia for three months or less to apply for an ETA at the same time as they make other online travel bookings

See also:
Fact Sheet 55 - The Electronic Travel Authority

        ETA arrangements are currently available to eligible passport holders from 33 countries.

        Only Australian citizens have automatic right of entry to Australia. All other non-citizens, including people who migrated and now live in Australia permanently, must hold a valid visa or authority for re-entry to Australia. New migrants are issued with a multiple re-entry visa when their immigration to Australia is approved. These visas last up to five years from the date of grant. After the initial visa has expired, if the holder wishes to continue to travel to and from Australia as a permanent resident, they must obtain a Resident Return Visa (RRV).
See:
FAQ - Resident Travel

        The 1973 Trans-Tasman Travel Arrangement allows New Zealand citizens to enter Australia to visit, live and work. You need a valid New Zealand passport to enter Australia. You do not need to seek a visa before travelling, unless there are medical or character concerns. New Zealand citizens with medical conditions or criminal convictions should approach the nearest Australian diplomatic office overseas to discuss their entry to Australia before travelling to Australia.
All other New Zealand citizens will need to present a valid New Zealand passport for immigration clearance in Australia. You are considered to have applied for a visa and, subject to health or character concerns, will automatically receive a Special Category Visa (SCV) which is recorded electronically. Your New Zealand passport is stamped, showing the date of arrival in Australia. This is the only evidence provided or necessary to show you are a holder of an SCV.
There is no need for a New Zealand citizen who holds an SCV to apply for, or be granted, permanent residence in Australia unless you wish to access certain social security payments. The SCV allows a New Zealand citizen to remain and work in Australia lawfully as long as you remain a New Zealand citizen.
See also:
Fact Sheet 17 - New Zealanders in Australia

        Your visa may cease when you leave Australia. If you intend to return to Australia you should check before you leave whether your visa will permit you to return, and the time limit for returning to Australia that applies in your case.