The egg crate method is typically used for static models. Most common amongst full hull, but could just as well be used for waterline models. The benefit over Bread-and-Butter or Solid block model boat hull is that the tedious template-fitting-procedure is more or less built into this method of construction.
The principle is to cut out the bulkheads, a keelson and one or more "decks" (actual or false). The material for the hull structure can be made from balsa, styrene, basswood or even card stock, or just about anything else you can think of.
The voids are then filled in with blocks of carving material of your choice. Most common are Balsa, Basswood or Styrene foam – but the field is wide opened.
Some builders may suggest using a harder material for the skeleton than the filler, but there are pros and cons to doing that. On the plus side, you're less likely to remove too much material from the shape defining ribs and backbone.
On the negative, if the structure isn't perfectly true, you won't be able to correct it as easily by sanding a little extra at the high spots.
I tend to recommend a happy medium - make the skeleton of something slightly harder, but not excessively so. Good combinations include: Styrene sheet structure with light insulation foam filler, hard balsa or basswood sheet structure with light balsa filler etc.
When the block material is glued in, it is good practice not to apply any glue to the bulkheads themselves and use modest amounts of glue in general. Apply it away from the boundary edges between blocks and structure. You want to avoid squeeze-out at all cost.
The reason is that the difference in hardness between the filler block material and the glue will make you sand too hard and gauge out the blocks, leaving hard ridges where the glue-lines are. It is virtually impossible to make the hull smooth. Instead, secure the blocks with glue away from the edges of the "egg crate" structure.
The downside is that the hull structure is time consuming to build. It is also very important that the templates that the structure is made from are accurate and true – otherwise you will have to free-lance the last bit before you have a smooth hull.