MIT Whirlwind is in some ways ancestor to all modern computers by switching to bit-parallel architecture with multiple bits being handled at a time.
36bit word length became common for scientific applications because it was apparently considered enough to do equivalent of 10 digit precision in fixed precision arithmetic, thus common pattern of 36 among American scientific computer lines.
Later common availability of 4bit components like 74xxx families meant that multiplies of 4 bits started being common.
4bits also allow to handle calculations in BCD form, which had obvious use cases in businesses, which is partially why S/360 which attempted to consolidate IBMs scientific and business lines went with 32bit word length - 8 bit was comfortably 2 BCD digits and also would fit one character of then-upcoming ASCII standard (the reason EBCDIC survives in S/360 is that ASCII was not yet ready and IBM decided to extend their existing codes instead of taking unfinished standard that could change - and they had to hardcode it in some devices back then)
The final nail in 36bit and longer word lengths was floating point becoming fast enough - and arguably infighting between VAX and PDP-10 groups at DEC which among other things triggered existence of BSD Sockets API and their horrible legacy on networking.