To add to the other answers you've gotten, "cycles" and "hertz" are both still used. The frequency (in Hz) is a count of how many cycles are in a one second period. A datasheet for an electronic device might have the frequency it's compatible with listed on it (typically 60Hz in the US, 50Hz in Europe).

For some signal processing and protection equipment you'd also see a number of cycles listed on the datasheet - that will always be paired with a "at X Hz" clarification, because it's functionally telling you how long the device takes to operate. For utility line circuit breakers, for example, "3 cycle" and "5 cycle" breakers are the most common options in the US, where 3 cycles translates to "this breaker will be fully open within 3/60 of one second of a trip command."