Eliot Coleman addresses soil blocks in his book "The New Organic Grower".
There are many advantages to soil blocks. I have the mini 3/4", the 2", and the 4" blocker. Peppers, tomatoes, lettuce, and herbs is mostly what I start in the 3/4" blocks. Onions and Leeks could also be started in the mini blocks. Most everything else I start in the 2" blocks. This would include cabbage, peas, beans, melons, corn, squash, etc. There are a few things I do not use blocks for at all including carrots. Some of these root crops need the depth for getting a good start. This is why it is recommended to direct seed them.
Some advantages:
Mini Blocks: allows for larger amount of germination if using a heat mat. You can get quite a few blocks on a small heat mat to get them germinated saving you the money of having to buy larger or multiple heat mats. They also warm faster being real small. You put only one seed on each block. If one does not germinate, you just put that block back in your mix and reuse it. You can also put another seed on it if it is holding up ok. The only disadvantage to these blocks is keeping them moist. You have to spray them several times a day to keep them from drying out.
Blocks in general:
The roots of plants sown in soil blocks will grow until they reach the edge of the block. Here they pause until they are potted on. After being potted on to the next size or into the garden, the roots can continue to grow naturally. Inside of plastic containers and peat pots the roots continue to grow around the edge of the container. When they are placed into the garden they do not reach out as quickly to establish a good root system.
You also don't have the expense of buying peat pots or plastic starters every year. You can do a search on soil blocks and get more information on them.