Process models describe the behaviour of a system, as opposed to ER models which only describe the data used within a system and how that data is related to one another.  Process models therefore bring a system description 'to life' and are generally regarded by users as being  more helpful in validating a system's requirements than an ER model.

Each process model can be used in two ways- it can either describe how a system currently works (current logical model) or it can describe how a system will work in the future (future or new logical model).

DFDs and STDs can be used to describe the control aspects of a system

It is normal for analysts to omit control details from a data flow diagram (DFD).  This is an example of the process of abstraction in which detail is deliberately omitted to aid clarity.  Analysts what clarity because they are seeking to understand what a system must do, rather than how it will do it.

It is only at the design stage of a system, that designers would add control process, control flows and develop state transition diagrams (STDs) to describe how and when the system will perform particular actions.

Structured Design requires a degree of intuition to go from DFDs to structure charts

Unlike data flow diagramming, there is no obvious way to map analysis products (such as DFDs) into design products (such as structure charts).  It is more a process of intuition and use of general guidelines.  This is one of the weaknesses of the structured analysis and design process.