Underwater Acoustic Sensor Networks (UASNs) is a prominent field in communications due to several applications. UASNs enable underwater data collection and monitoring in different applications. UASNs face several challenges like node mobility, low bandwidth, high energy consumption, and routing. The complexity of the underwater routing is increased due to node mobility. Several underwater routing protocols exist in the literature; they determine next-hop based on different criteria. Some criteria to select next-hop are link quality, residual energy, hop-count, etc. Many underwater routing protocols either use hop-count or hop-count as one of the criteria to choose nexthop. Such routing protocols result in lower hop-count, resulting in smaller end-to-end delays. These routing protocols are instrumental in the delay-sensitive applications where the endto-end delay is the primary requirement. However, maintaining up-to-date information of the hop-count of nodes is one of the major challenges due to frequent changes in underwater topology caused due to the water current. This survey paper focuses on underwater routing protocols based on hop-count in selecting the next-hop. It focuses on updating hop-count information in various hop-count-based underwater routing protocols.