What to do? Demolish or modernise legacy monoliths?

For over sixty years, we have been building software that is becoming ever larger and more complex. Not only do we now have legacy mainframe systems, but the systems in object-oriented programming languages have also grown so quickly and uncontrollably over the last twenty years that they have become a big ball of code. All this legacy code is driving up development costs and making us reluctant to touch these old software systems. Is this unavoidable? Or is there also good legacy?