The Use of CGI in Films

You can use Computer Generated Imagery in various ways; filmmakers in particular have become a lot more reliant on it within the past 15-20 years.
With the advancement of technology in today's society, it has become easier to visualise and create fantasy settings which predated technology could not have handled.

Despite this, some films such as Labyrinth (1986) managed to create a fantasy setting with clever costume and make up designs without much technology.

To the left is an example of how they moulded the material around an actor to create the illusion of a monster.

This shows good use of materials for the time this film was made, but it could not have achieved computer generated imagery, simply because that advanced technology wasn't invented yet.

Ludo from the film Labyrinth, an elaborate costume

Compared to costumes, computer generated imagery has proven to be cost effective and allows the filmmaker to create anything they visualise, whereas with big costumes and make up, a lot of materials go into producing what the artist wants.
In recent films such as the Harry Potter franchise, a lot of fantasy creatures and beasts were needed to bring the film to life. The easiest and cheapest way for them to achieve sufficient images was through CGI.
An example of this is the basilisk in '...The Chamber of Secrets'. A model of the creature, roughly the right size, would be made for the actors to interact with on set, then the motion would be man made through the use of CGI.

Basilisk model

Final shot from the film

A similar technique was used in their third film '...The Prisoner of Azkaban' with the hippogriff being created as a model then animated later on. 

Hippogriff Model

Shot from the film 'Harry Potter'

A limitation to CGI could be when working with actors, they obviously can't feel the computerised creatures they are supposed to be working with on their stage, so to get the best performance out of the actors, models have to be made to interact with, which will cost the team money to build.

Even with this in mind, the high quality of the animated creatures proves that the investments into the film were worth it and will ultimately look more impressive on the big screen.