YAK42 wasn't made to replace TU154 or TU134, actually. The aircraft is more or less in a class by itself, operating from the more primitive airfields in Russia and with a passenger capacity and range that best suits it to short-range flights. I think it is the closest design to today's regional jets, but came long before their time.
The YAK42 was the second Soviet type to be withdrawn from service due to unexplained crashes. Not long after its introduction into service in the mid '70s, there were several crashes which later were determined to be the result of design flaws in the aircraft's flap system. The design was modified and re-introduced as the YAK42M.
The current models suffer from the maladies of all Soviet-era jetliners - overly thirsty engines and primitive passenger accommodations. I've heard there is a newer version, YAK242, under development which has twin engines and EFIS cockpit, but this may have been abandoned. There hasn't been anything new from Yakovlev for quite awhile.
A re-engineing program was studied for both the YAK40 and YAK42 which would have involved rebuilding the tailfin and tailcone, thus eliminating the centre engine, and equipping YAK40s with Lycoming turbofans, and YAK42s with CFM engines. Due to prohibitive cost, much like the CFM re-engine program for IL86, this program was dropped.