There's been talk of a future RN carrier around the size for the Ford Class, but to date the RN functions much like its previous iteration the Soviet Navy. It's still centered around long-range strike capabilities to keep NATO - and especially US ship - outside of the effective range of air defense missiles like SM-6 and beyond the reasonable fire-range of long-ranged anti-ship missiles like Tomahawk block IV and LRASM.
Reasonable fire-range means the distance the US will actually fire from. Even with a 1000+ km range, the US wont fire a Tomahawk from that distance targeting a move ship. They just wont do it.
The current trend with the RN is building smaller, but heavily armed frigates packed with long-range anti-ship and land-attack missiles. Missiles like 3M-54.
Their aircraft remain as they always have, being a healthy mix of TU-22M3, TU-142MK/MR/MZ and SU-27/33 series aircraft carrying long-range anti-ship missiles.
Both Oscar II and Yasen provide Russia with much the same. Standoff land and ship attack capabilities, though the Oscar IIs are getting a bit old now:
And interesting trend that Russia's been implemented - or at least trying to - is a shift towards expeditionary warfare, for assaults against near by targets. Russia's attempted purchase of several Mistral class amphibs:
And the creation of new landing craft, the Dyugon class:
Indicates we may be seeing a shift towards an expeditionary capability, in conjunction to strategic deterrence and a continued focus on anti-shipping.
Russia is also beefing up its special operations capabilities, another sign of a continued trend from Crimea, by introducing new special warfare craft like this Project 03160 ‘Raptor’, which has been spotted in Syria:
All in all the RN remains the same in some respects and is undergoing changes in others. It's capabilities against a NATO-type target remain as they've always been with tactics and doctrine largely unchanged. But Russia is evolving too and is slowing gaining a greater capability to project power and implement a "shadow" war type of scenario, as noted in both Syria, Ukraine and Crimea... if only near its own borders.