This paper introduces four versions of an international bilateral migration stock database for 226 by 226 countries and territories. The first three versions each consist of two matrices, the first containing migrants defined by country of birth, that is, the foreign-born population; the second, by nationality, that is, the foreign population. Wherever possible, the information is collected from the 2000 round of censuses, though older data are included where this information was unavailable. The first version of the matrices contains as much data as could be collated at the time of writing but also contains gaps. The later versions progressively use a variety of techniques to estimate the missing data. The final matrix, comprising only the foreign-born, attempts to reconcile all of the available information to provide the researcher with a single and complete matrix of international bilateral migrant stocks. The final section of the paper describes some of the patterns evident in the database. For example, immigration to the United States is dominated by Latin America, whereas Western European immigration draws heavily on Eastern Europe, Central Asia, and the Mediterranean region. Over one-third of world migration is from developing to industrial countries and about a quarter between developing countries. Intra-developed country and intra-FSU (former Soviet Union) flows each account for about 15 percent of the total. Over half of migration is between countries with linguistic ties. Africa accounts for 8 percent of Western Europe's immigration and much less of that to other rich regions.