last century; previous century
Refers to the century immediately before the current one, or a past century in a sequence. Common in historical and news contexts.
At the end of the last century, the internet spread rapidly.
This building was built at the beginning of the previous century.
Used loosely or figuratively to refer to a bygone era, often with a nuance of being outdated or old-fashioned. Less common than the literal 'last century' sense.
That way of thinking is like a relic of a bygone era.
今世紀 refers to the current century, while 前世紀 refers to the century before it.
Compound of 前 (zen, 'before') + 世紀 (seiki, 'century'). The literal meaning is 'previous century', with an extended figurative use for 'old times'.