Bismuth is added to Sn–Ag–Cu-based solders to increase strength and solder joint reliability but accelerated thermal cycling (ATC) tests have shown variable thermal fatigue performance. To better understand their thermal fatigue mechanisms, we investigate three Sn–Ag–Cu-Bi solder alloys containing between 3 and 6 wt.% bismuth in two types of ball grid array (BGA) packages tested using a harsh ATC profile of -55/125 °C. We study how the bismuth additions affect the microstructure after soldering, after ~ 4 years storage at room temperature and after thermal cycling. The Weibull reliability statistics are then correlated with the microstructural evolution including solutionising, homogenisation, bismuth precipitation, recrystallisation and crack paths. The results show that high strength Sn–Ag–Cu-Bi solders can improve the resistance to thermal fatigue, but high solder strength needs to be balanced against excessive stress transfer to the intermetallic attachment layer.