The way unemployment is calculated has not changed. It is the measure that is boasted as "Unemployment" that is suspect. This is because the unemployment rate is defined by the Bureau of Labor Statistics as:
People are classified as unemployed if they do not have a job, have actively looked for work in the prior 4 weeks, and are currently available for work.
So, for the Civilian Labor Force, 159,463,000 individuals, 7,849,000 are counted as unemployed, setting the 4.9% value.
The Rub is that the total population of non-institutionalized Civilians is 253,854,000, meaning that 94,391,000 persons aren't considered in the labor force. Of those, 5,833,000 want a job. Labor Participation rate is at 62.8%, a value not seen since the late 1970's.
Going beyond the 4.9% value, deeper into the Bureau of Labor Statistics analytics, there are five other numbers that evaluate unemployment.
The "real" value that people claim should enjoy more credence than 4.9% is the U-6 number, of 9.7%. The U-3 value, 4.9%, only accounts for "Total unemployed, as a percent of the civilian labor force (official unemployment rate)." Per the above, U-6 accounts for "Total unemployed, plus all persons marginally attached to the labor force, plus total employed part time for economic reasons, as a percent of the civilian labor force plus all persons marginally attached to the labor force." U-6 is considered more inclusive, accounting for the unemployed, underemployed, and those discouraged from looking for a job.