In 1434 the Strozzi lineage had held a leading position in Florentine society and government for at least one hundred and fifty years, and was one of the largest and wealthiest of the city's patrician lineages. The records of the catasto of 1427 and of the scrutiny of 1433 are used to give a profile of the dominant social, economic and political position of the Strozzi before the advent of Medicean dominance. Their record of electoral success, and the political and cultural leadership of influential and respected men such as Palla di Nofri and Matteo di Simone, with other factors, put the Strozzi amongst the greatest enemies of the victorious Medicean regime of late 1434. The effects of political opposition and exile on the lineage are examined both directly, through records of office-holding, and indirectly through such indicators as marriage alliances and household wealth. The two most prominent lines of the Strozzi were exiled after 1434. Palla di Nofri's life and preoccupations in his Paduan exile are examined, together with the lives of his sons; none of these Strozzi ever returned to Florence, pursued as they were by the enmity of the Medicean regime. The very different careers of Filippo di Matteo and his brother Lorenzo are also examined: how they succeeded in founding a lucrative bank in Naples, and in returning to Florence to 'rebuild' (rifare) the position of the Strozzi lineage there. The final decades of the century saw the Strozzi in an economically more secure position, due substantially to the efforts of Filippo. Except for a very small number of its members admitted into the regime, most of the lineage is here shown to have remained excluded from significant political office until after the fall of the Medici regime in 1494.