Huawei Technologies Co. may be unknown to many U.S. consumers, but the Chinese company is becoming a threat to Samsung Electronics Co., the world's biggest smartphone maker.

Huawei's rise is an indication that growth in the mobile-phone industry is coming mainly from outside China—emerging markets where many consumers are still replacing basic feature phones with smartphones. While China's increasingly saturated smartphone market is showing signs of slowing growth, Huawei is expanding rapidly in Africa, the Middle East and...