My 19 month old started doing this a few months ago, and I was mortified. The pediatrician and all those baby books out there don't want a child out of the crib until around 3, and I absolutely agree! Especially with my 19 month old, and your 20 month old, the last thing a mother wants is a screaming tantruming toddler capable of getting out of bed and running around wherever he or she wants wreaking havoc in the rest of the house. I am a child psychologist, and frankly, people that choose to put their toddlers into toddler beds when they start climbing out at such a young age is asking for worlds of trouble - often, toddlers that are allowed to sleep in toddler beds generally regress as far as sleeping goes: children that have slept 12 hours a night in their crib are suddenly getting up 5 times a night to wake everyone else up, and then everyone ends up angry and cranky from lack of sleep. So ABSOLUTELY do not even entertain the idea of putting him in a big bed (though many mothers on here will suggest you do so). Our children are at an age where they do not have the capabiity of controlling themselves and their compulsions, and are unable to really understand why they shouldn't get out of bed if they physically can. SO, that being said, this is how we solved the crib climbing problem:
BUY A CRIB TENT!!! It was the best money I ever spent. Its a mesh tent that is completely see through and attaches to the crib itself with velcro, and zips open and closed. The mattress actually fits into the mesh tent itself, so it also keeps angry toddlers from throwing all their stuff out of the crib and onto the floor when they are pushed out of shape. It also keeps them from getting out, as well as getting their legs stuck in the crib slats. My daughter actually really likes it - its her special little fort, and I sometimes put a blanket on the top of the tent, which she LOVES. She is back to her normal, happy sleeping habits now, and I dont ever have to worry about her getting out, throwing out her blankie or binky, getting stuck, or anything like that. It is very easily assembled and disassembled, so you can take it with you on trips, and even mommy can take it off and on very easily by herself. When my daughter is old enough to handle a toddler bed, then she will have one, but until I am SURE she is ready (which probably wont be until around 3 for most children) the crib tent has been a godsend.
You can buy them at most baby supply stores such as babies r us. They are a little pricey ($50-$75) but the money is WELL worth calm and happy nights sleep for the next year for the entire family.