Under Seat Steering (USS)
The handlebars on a recumbent may be mounted below the rider so that their arms hang in a relaxed position. Known as under seat steering (USS), this is arguably the most comfortable and least tiring steering position since you’re not reaching up to grip the handlebars. That said, it can be a bit trickier mounting/dismounting a bike with USS without practice, and you’ll be less aerodynamic when riding since you’ll have a wider profile against the wind. It’s also worth noting that USS is more mechanically complex and expensive, often requiring non-standard bike parts including a tie-rod to link the bars to the fork (known as indirect steering). There are a few USS bikes out there with direct USS steering where the handlebars connect directly to the steerer with a stem (just like a regular bike but inverted), but the handling can be a bit too twitchy with direct USS steering. In contrast, indirect steering often allows the rider to fine tune the feel of their steering by changing the placement of the tie-rod to adjust the steering ratio.
Personally I’ve found USS to be the ultimate design in recumbent comfort. My first recumbent came with above seat steering (ASS- see next section below), and I immediately had to switch it to USS because my elbows were giving me problems. Despite the comfort, USS did get annoying when I needed a good place to mount accessories like my GPS. Having USS also made it harder to walk my bike since I had to bend over it a bit to steer it, and I needed a wider space for parking or storing the bike. My elbow pain improved a few years later after a couple surgeries (cubital tunnel release and ulnar nerve transposition), and I did switch back to ASS without much of a problem mainly for the sake of convenience.
If you’re interested in USS bikes, you have a few options in the US including Azub, HP Velotechnik, Linear Recumbents, and Long Bikes. In Europe you’ll have a few more options with Challenge Bikes (Netherlands), Slyway (Italy), and Flux, Toxy, and Traix (all in Germany). Just note that the HPV Streetmachine and Toxy bikes use direct steering, and may be a bit more tricky to ride.
Above Seat Steering (ASS)
When the handlebars are mounted over the rider’s lap and they have to reach up to them, the bike is known as having above seat or over seat steering (ASS or OSS). Compared to USS, ASS is more aerodynamic and generally easier to learn. You’ll have some choices regarding the shape of the handlebars: “praying hamster bars” that keep your arms in a tight position close to your chest versus “superman bars” where you are gripping onto wide bars in what is called an “open cockpit”. The superman bars are more ergonomic since they keep your hands/wrists in a neutral position where you don’t have to rotate your wrists to hold onto the handlebars. ASS does require your arms and shoulders to be more engaged compared to USS, so your arms will tire after a while. Unlike USS, you’ll have plenty of room on the handlebars to mount accessories such as mirrors, bells, and lights, but you may also have worse visibility with the handlebars blocking your line of sight (especially if you are in an extreme horizontal position).
There is a less common type of steering out there known as pivot or center steering. On these bikes, there’s a pivot at the center of the bike, allowing you to steer the front wheel by leaning. These bikes may come with side bars to help you lean into a turn, and may have no handlebars at all! I’d love to try such a bike one day, but the only center steering bikes I’m aware of are old Flevobikes from the Netherlands.