To cope with an interrupt, the CPU suspends the current running process. Interrupt service is the term for this. How can we know why the current procedure is being halted in the first place? Why can't...

To cope with an interrupt, the CPU suspends the current running process. Interrupt service is the term for this. How can we know why the current procedure is being halted in the first place? Why can't we just continue the current process and then deal with the interruption later? Alternatively?