Infinitives are forms like write, work, build and break. They are often used with the marker to. The infinitives are used in the following structures.

After be

The infinitive is often used after the different forms of be (is, am, are, was and were) to talk about an agreement or arrangement. It is also used to ascertain the wishes or orders of someone else, or to express a complaint.

We are to start the project tomorrow.
He is to arrive by the evening flight.
The committee is to meet on the 12th of this month.
John and Mary are to be married next month.
How long are we to wait like this?
The keys were not to be found anywhere.
When am I to finish this job?

The structure be + to-infinitive is often used to express a command.

The scouts and guides are to wear their uniforms for the parade.
You are to take this medicine whether you like it or not.
Father says that you are not to stay up late.

The subject + verb + object + infinitive

In this construction the infinitive expresses a finished action.

We saw the mother beat her child.
I watched him play.
Newton saw the apple fall to the ground.
We saw the burglars break open the house.
They made the child drink the milk.
Did anyone see him leave the house?

Note that after see, hear, make, notice and watch, we use an infinitive without to.

He made me wait. (NOT He made me to wait.)
We heard her sing. (NOT We heard her to sing.)

The Subject + Verb + Object + Present Participle

In this construction the present participle indicates an action that is going on and not completed.

Compare:

I watched him play. (I watched the whole action.)
I watched him playing. (I didn’t watch the whole action.)
Newton saw the apple falling to the ground.
We saw the mother beating her child.
We observed them rehearsing the play.
I could smell something burning.
We watched the ship steaming slowly away.
We heard them singing in the next room.