Dirt, dust and grime build up quickly in a frequently used kitchen, but the knife block is likely one of the items that you rarely check while cleaning. Dust lands in the gaps between knife handles, sauce might splatter from the stove and grime or crumbs can build up inside the knife slots. The narrow slots might initially present a cleaning conundrum, but you likely have all the tools you need to clean the knife block.
Dust and Debris
Remove all knives and set them aside or run them through the dishwasher while you clean the knife block. Hold the knife block upside down over your garbage can or kitchen sink. Shake it a few times and tap on the bottom to knock loose any loose crumbs inside. Use your vacuum cleaner's crevice tool or an electronics vacuum to remove the dirt and dust from the top and around the edges of each slot. A can of compressed air works well to blow dust and crumbs out of a knife block -- hold the knife block upside down and insert the can nozzle in the slots.
Scrub the outside of the knife block with hot, soapy water. Flush inside the slots with the soapy water. If you detect some grimy buildup inside, use pipe cleaners or a thin wire brush to scrub inside the slots. Submerge the knife block in your sink's basin to loosen tough buildup. Rinse the knife block thoroughly so leftover soap residue doesn't attract more dirt. Sanitize in undiluted white vinegar or a solution of 1 tablespoon of bleach per 1 gallon of water. Set the knife block upside down to air-dry or use a hairdryer to dry inside the slots.