A deep problem in analytic number theory is to understand correlations of general multiplicative functions. In this talk, we derive correlations formulas for so-called bounded “pretentious” multiplicative functions. This has a number or desirable consequences. First, we characterize all multiplicative functions with bounded partial sums. This answers a question of ErdH{o}s from 1957 in the form conjectured by Tao. Second, we show that if the average of the first divided difference of multiplicative function is zero, then either
for
or
is small on average. This settles an old conjecture of K’atai. If time permits, we discuss some further applications to the related problems.