Records of passenger lists can be found in a number of places. Whilst official lists are often held in national archives as part of national collections, there are hundreds of other sources on the internet

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Australian Passenger arrivals index, 1921-1949
Search for passengers arriving by ship in Fremantle and other Western Australian ports between 1921 & 1949; or arriving at Perth airport between 1944 & 1949.

British convict transportation registers 1787-1867
Details for over 123 000 of the estimated 160 000 convicts transported to Australia in the 18th and 19th centuries including names, term of years & transport ships.

Castle Garden Immigration Database

Passenger Lists on the Internet

Highlands & Islands Emigration 1852-1857
Searchable database of almost 5000 individuals who left western Scotland for Australia. Extracted from the National Archives of Scotland's Highland Destitution series (HD).

Scottish Emigration Database
Records of over 21,000 passengers who embarked at Glasgow and Greenock for non-European ports between 1 January and 30 April 1923, and at other Scottish ports between 1890 and 1960.

Ships & Passenger Lists of Polish WW2 Refugees arriving from Africa and Europe
Lists compiled by a former Polish D.P. (Displaced Person).

UK Incoming Passenger Lists 1878-1960
Passenger lists of ships arriving in the United Kingdom from foreign ports outside of Europe and the Mediterranean from 1878-1888 and 1890-1960.
 
UK Outward Passenger Lists 1890-1960
Passenger Lists for long-distance voyages leaving the British Isles. The index includes not only immigrants and emigrants, but also businessmen, diplomats and tourists. Images of the passenger lists are available for a fee.