There are a few issues with underground cable but the main ones are insulation and protection against damage by crushing or distortion caused by shifting earth due to subsidence or, for example, compaction due to traffic, etc.
Figure 1. An SWA cable (left) showing the 3-phase + N conductors, individual insulation, overall insulation, armour and outer sheath. The image on the right shows the armour compression gland attached and the earth lug terminal. Source: ETS Cable Components.
For low voltage power distribution (< 1,000 V) steel-wire armoured (SWA) cable is most common. Insulation will be PVC type. (See Figure 1.)
Figure 2. Note the oil ducts in this cable. Source: Brownfield Site Solutions (UK).
For high voltages (> 100 kV) used on underground transmission lines oil-filled paper based insulation was common but many newer installations are using XLPE. The oil-filled insulation had to be kept "topped-up". This means that some sort of reservoir has to be used and generally installed to feed in at the high-points of the cable route so that gravity will keep the cable oil-filled. A further complication is that on a long climb that the pressure inside the cable must be limited to prevent rupture so segregation of the cable into pressurised sections is required.
Figure 3. 115kV G&W Oil Filled Straight Joint. Source: Cable Joints (UK).
Since underground cables are so much more bulky than overhead type due to their insulation there is a limit on cable lengths that can be transported to site - 750 m, for example. This means that many joints are required and these may be laid out to suit the oil filling. Underground joint chambers may be required for high-voltage cables. Note that very little, if any, of this is appreciated by objectors to pylon routes. It is difficult to beat the free insulation provided by air.
Nexans Underground Cable Catalogue looks like an excellent primer on medium voltage (3 - 36 kV) cables.