The fashion industry is currently swept up in a storm of nostalgia. While mom jeans, platform sneakers and other '90s trends used to be considered outdated, now they are all the rage.

Riding on this throwback wave, Italian heritage brand Fila and American sweatshirt producer Champion are enjoying another lease of life.

Fila's signature red, blue and white color palette and Champion's embroidered "C" — both of which have been around for a century — have garnered attention as the demand for nostalgic, iconic designs rapidly rise.

"The 90's retro trend is very hot right now and Fila and Champion are at the center of it," said Matt Powell, a senior sports industry analyst at the New York-based research firm NPD Group.

From 2016 to 2018 alone, Fila's sales increased 205% from 967 billion Korean won (U.S. $821 million) to 2954 billion Korean won (U.S. $2.51 billion). Fila Korea became the brand's global headquarters in 2007 after acquiring the rights to Fila's global subsidiary company, Sports Brands International, along with the entire global business.

Champion's 2018 sales excluding the U.S. mass channel amounted to $1.36 billion, up from approximately $1 billion in 2017. The CEO of Champion's parent company, Hanesbrands, also recognized the sports brand as a "growth initiative" which delivered "stronger than expected" results in its 2018 fourth-quarter earnings call.

Compared to main industry players such as Nike and Adidas, the two are smaller, unique brands — which are winning right now and growing faster than the industry, Powell told CNBC.

"The younger consumer wants to wear unique products, made by unique brands and sold in unique retailers," he added.