Set out below are details of the equipment I use, as well as links to a few resources that may be useful in selecting the appropriate lens, camera, housing and strobes for underwater photography.
My current underwater set-up is based around a Nikon D850 (FX, full frame) in a Subal housing, however the majority of images on my site were captured using a Nikon D700. I've always used Nikon cameras. There seems to be a disproportionate number of underwater photographers using Nikon equipment, potentially as a legacy of Nikon's support for underwater photographers through their Nikonos range from the 1960s to 1990s.
For wide angle photography I often use the Nikon 16-35mm F/4G ED VR. This is an excellent lens for landscapes and underwater photography of large animals that will not let you in close enough to use a wider lens, or animals the size of turtles and seals.
For larger animals (whales, large close-range sharks) I typically use a fisheye lens (see below).
I use the 16-35mm with a Subal port extender and a 9 inch Zen Underwater dome.
Most of my recent wide angle photography is with the Sigma 15mm f/2.8 EX DG Diagonal Fisheye lens. This is an outstanding and relatively cheap lens with enormous depth of field (forgiving when focusing under pressure) and the ability to focus on objects ~10cm away from the dome. The lens is also very versatile, with the close focal distance allowing subjects that would typically require a macro lens to be captured.
Despite the fisheye lens downside of barrel distortion (spherical warping of the image), fisheye lenses often provide much more interesting compositions by allowing you to capture the primary subject, foreground and a sunburst all in the same image without much effort.
I use the Sigma 15mm with the 9 inch Zen Underwater dome with no port extender.
For macro photography, and some out-of-the-water portrait photograph, I use the Nikon 105mm f/2.8 VR G lens. This lens is often regarded as better suited to full frame cameras, but I've have got good results from it on a crop-sensor camera. Although this lens does tend to hunt (cycle in and out searching for a focus), the bokeh (intentional blur) is outstanding.
I use the 105mm in the Subal flat port with focus wheel.
In general, crop-sensor DSLRs are easier to use and produce better macro images than full frame DSLRs, due to the greater magnification. Many of the macro images on this site are taken using a Nikon D200 (DX, crop-sensor) and Nikon 105mm f/2.8 VR G lens.
For surf photography I use the Sigma 15mm f/2.8 EX DG Diagonal Fisheye lens in an SPL Waterhousing. I fix the focal distance manually to around 50cm, depending on the available light and other chosen settings. Hyperfocal distance relates to the distance that generates a near infinite depth of field and can be calculated using the link below.
For underwater lighting I use two Ikelite sub-strobes (1x DS160, 1x DS125). I shoot with strobe on manual, typically at less than 50% power. My preference is for a more natural lighting effect, and therefore use minimal strobe light on wide angle to fill in shadows and provide extra detail.
I try to keep my strobes on as low a setting as possible for macro photography, particularly with more delicate subjects that could be disturbed by the light.
For landscape photography I use the Nikon 16-35mm F/4G ED VR. Lee graduated neutral density filters are used in many of my landscape photographs. I use a Really Right Stuff tripod with the BH-55 Ballhead.
Underwater photography retailer Reef Photo’s knowledge base is very useful. The staff are also very helpful in providing guidance on the right setup.
Alex Mustard is an excellent underwater photographer who is generous in sharing his equipment knowledge and techniques.
Underwaterphotography.com has a wealth of information on equipment.