1) N-UNCOUNT Running is the activity of moving fast on foot, especially as a sport.

We chose to do cross-country running.

...running shoes.

2) N-SING: the N of n The running of something such as a business is the managing or organizing of it.

...the committee in charge of the day-to-day running of the party.

3) ADJ: ADJ n You use running to describe things that continue or keep occurring over a period of time.

He also began a running feud with Dean Acheson...

The song turned into a running joke between him and the press.

4) ADJ: ADJ n A running total is a total which changes because numbers keep being added to it as something progresses.

He kept a running tally of who had called him, who had visited, who had sent flowers...

So far, his running total in transfers fees is ₤12million.

5) ADV: n ADV You can use running when indicating that something keeps happening. For example, if something has happened every day for three days, you can say that it has happened for the third day running or for three days running.

He said drought had led to severe crop failure for the second year running...

She changes her look so often that she never seems the same woman two days running.

in a row, on the trot
6) ADJ: ADJ n Running water is water that is flowing rather than standing still.

The forest was filled with the sound of running water...

Wash the lentils under cold running water.

7) ADJ: ADJ n If a house has running water, water is supplied to the house through pipes and taps.

...a house without electricity or running water in a tiny African village.

8) PHRASE: usu v-link PHR If someone is in the running for something, they have a good chance of winning or obtaining it. If they are out of the running, they have no chance of winning or obtaining it.

Her role in Death and the Maiden, which put her in the running for the Laurence Olivier Award,...

Until this week he appeared to have ruled himself out of the running because of his age.

9) PHRASE: V inflects If someone is making the running in a situation, they are more active than the other people involved. [mainly BRIT]

Republicans are furious that the Democrats currently seem to be making all the running.

10) PHRASE: v-link PHR, PHR after v If something such as a system or place is up and running, it is operating normally.

We're trying to get the medical facilities up and running again.

English dictionary. 2008.