I was an illustrator for almost 25 years. Some of that time I worked as a fully-employed in-house newspaper illustrator, but for 5 years I worked for myself, and those were the really tough years! The advantages/disadvantages I have listed above concern freelancers, who are by far the majority. To be successful you need to be an enthusiastic self-starter - someone who has loads of ideas for projects to keep busy when the phone isn't ringing. These pot-boilers might be illustrations for a children's' book or new work to put in your portfolio to sell yourself to an editor.
There are different levels of work commissioners. When you are fresh out of college, or just starting up, the work that is more likely to come your way is from non-commercial publishers, those that do textbooks for schools or trade magazines or printing card companies. Work can also be picked up from international bidding sites, but the pay tends to be undercut and is not for everyone. The middle-range work includes big book publishers, newspapers, magazines, designers, public relation companies and the like. Advertising is where the high-end work comes from, where many thousands of pounds can come your way for even the smallest job. These jobs tend to go to well-established illustrators who have paid their dues.
Computers have changed the way artists work nowadays which is a blessing as well as a curse. The up-side is that it allows artists greater freedom to experiment with creativity, without the expense of art materials. You don't have to tear up your work if you make a big mistake. The down-side is that computer software has turned everyone into a potential artist, and the sort of private work that was once plentiful has now almost disappeared with the advent of "clip-art".
My own view regarding computer art is mixed: on one hand, it has taken art to a different dimension, with a greater capacity to create slick, perfect-looking art. Indeed, it has 'improved' the work of many lesser-talented artists, but at what cost? I sometimes wonder how many digital illustrators really know how to draw or paint with real art materials anymore. Have you noticed how similar digital art looks? The good news is that not all commissioners like digital art and genuine craftsmanship will one day return as a fashion.
The best part of working from home is sleeping in late, and being able to sit outdoors on a sunny day! The worst part is the loneliness - unless you have a family in the background to cheer you on or a wide network of pals. So be prepared.
Illustration is not a career that will make you a fortune, but if you are successful you can make a reasonable living doing something you love, and few people are lucky enough to achieve that.