Politics within the Sangha Where there is a group of people, there will be politics and organizational dynamics. This should be no different with the Sangha.

For example, monks trying to cause dissent or schism, monks who disobey instructions, monks trying to gain power over others, monks who are envious of others, monks trying to get the attention of the Buddha or their abbot etc.

How did the Buddha handle such situations in his time?

How are such situations handled within the Sangha today?
How did the Buddha handle such situations in his time?

There are two famous schisms in the time of the Buddha; the Devadatta schism and the Kosambi schism. 

In the former case, new, inexperienced monks were led astray by bogus teachings and the Buddha sent his two chief disciples to explain the truth to them. 

In the latter case, the Buddha tried to invoke the seventh means of settling disputes (adhikaranasamatha), called "covering over with grass" - i.e. agreeing to leave the past transgressions behind and start fresh. The monks refused and the Buddha abandoned them.

To some extent, it's not very instructive to ask "how did the Buddha handle X", since he was fully enlightened and knew how to best deal with every specific situation. Better to ask is how the Buddha taught one should deal with sangha politics. In this instance, he left fairly specific procedural teachings on how to avoid and deal with such affairs.

Briefly, the seven adhkaranasamatha for dealing with disputes and legal cases are:


Settling in front of the transgressor
Settling based on a confirmation of enlightenment
Settling based on a confirmation of insanity
Settling based on an admission of guilt
Settling by a vote of the majority
Settling on punishment for evil-doers
Settling by covering over with grass


Beyond this, there is specific and lengthy instruction in the vinaya regarding schisms, and there are various teachings on dealing with power struggles, envy, disobedience, etc. 

How are such situations handled within the Sangha today?

Rather poorly, for the most part. But "the sangha" is a huge and diverse conceptual body that for all intents and purposes doesn't exist as a single entity. Various sects, traditions, and even countries have their own sanghas now, and each sangha has its own means of dealing (or not) with such problems. For the most part, it is far more difficult to actually deal with monastic transgressions in modern times; without the stability of a large body of enlightened beings, it's much more "every monk for himself", unfortunately.