Free-space optical (FSO) systems are able to offer the high data-rate, secure, and cost-efficient communication links required for applications such as wireless front- and backhauling for 5G and 6G communication networks. Despite the substantial advancement of FSO systems over the past decades, the requirement of a line-of-sight connection between transmitter and receiver remains a key limiting factor for their deployment. In this paper, we discuss the potential role of intelligent reflecting surfaces (IRSs) as a solution to relax this requirement. We present an overview of existing optical IRS technologies; compare optical IRSs with radio-frequency IRSs and optical relays; and identify various open problems for future research on IRS-assisted FSO communications.