To fully understand the processes occurring in present-day living cells, we need to consider how they arose in evolution. The most fundamental of all such problems is the expression of hereditary information, which today requires extraordinarily complex machinery and proceeds from DNA to protein through an RNA intermediate.
How did this machinery arise?
The book Molecular Biology of the Cell, a classic in-depth text reference in cell biology (by Alberts B, Johnson A, Lewis J, et al.) which outlines some of the arguments in support of the RNA world hypothesis and discusses how DNA may have taken over as the genetic material, mentions the following conclusion:
One view is that an RNA world existed on Earth before modern cells arose. According to this hypothesis, RNA stored both genetic information and catalyzed the chemical reactions in primitive cells.
Only later in evolutionary time did DNA take over as the genetic material and proteins become the major catalyst and structural component of cells.
For further reading, click here to see a chapter of the book suggesting the early existence of an RNA world of living systems.