Concrete floors are not an esthetic shared by all but with the right setting and large area rugs, it can be a great look. The house above is in Arizona where the cool concrete floors make a lot of sense. The owners embrace a very modern look and the concrete works for them.

As for deep crack grime, I would rent a steamer and tackle the crud that way. Here are some concrete cleaning solutions that might work for you. Unsealed concrete is pourous and will absord oil etc.

A Heavy-Duty Floor Cleaner
Here's a recipe for a solution that will remove extra-tough dirt and grime from asphalt, glazed or unglazed ceramic tile, concrete, flagstone, and slate floors:

* Mix 1⁄4 cup low-sudsing, all-purpose cleaner; 1 cup ammonia; and 1⁄2 gallon cool or cold water. Caution: Wear rubber gloves, and work in a well-ventilated area when using this powerful solution.
* Apply the solution to the floor with a sponge mop, using pressure for heavily soiled areas; rinse with cool, clear water for spotless results.
* Dry with a soft cloth.

Concrete is an extremely strong, durable material made from cement and aggregate. Concrete is porous, whether used as a floor in garage, porch or patio, driveway or walks.

Often porch or patio floors will have an extra smooth surface, but it will still absorb stains easily. It may be sealed or painted. Concrete floors are sealed to prevent staining, since without sealing it absorbs stains readily. The floor must cure and dry after it is laid before it can be sealed, with the time required varying with weather, temperature, building conditions, etc. Floors must be clean, and any remaining alkali in the concrete must be neutralized before sealing. Contact a good paint store or cement dealer for complete instructions and materials to use.

Painting concrete varies depending on its use. Latex floor paints react with rubber tires in garages, as well as with bicycle tires, lawnmower tires, etc. The result is peeling. Alkyd floor enamels are more moisture resistant, and normally old up better under these conditions. But they are more slippery when wet. If there is moisture rising from beneath the surface of the floor it may also cause enamel floor paint to peel.

To clean, wet with clear water. Apply a hot solution of 2 to 2 1/2 ounces washing soda or 1/2 ounce TSP (tri-sodium phosphate) per gallon of water. TSP can be found in paint, hardware and home center stores.

Grease Stains: In a garage, it is advisable to place a shallow metal pan under the car to catch dripping oil. Spreading the area under the car with sand or sawdust will help absorb dripping oil. Periodically saturated sand or sawdust should be scraped away and fresh, clean material put in place. This will prevent tracking oil to other areas of cement or into the house. If oil or grease is spilled on porch or patio cement, apply an absorbent powder such as fuller's earth, cornmeal, or sawdust to absorb as much oil as possible immediately. Leave it on stain for a few hours and sweep up.

Here are some various methods to remove grease stains:

1. Using a stiff long handled brush, scrub stain with concentrated detergent suds. Rinse well with hose. Dry and repeat if necessary.
2. Sprinkle "dishwasher" detergent (dry) on wet concrete. Let it stand a few minutes; pour boiling water on area. Scrub and rinse. Use rubber gloves on hands.
3. Commercial products are available in paint/hardware home centers. Some can also be used on blacktop surfaces.
4. On wet oily surface of concrete, sprinkle with tri-sodium phosphate. Allow to stand 15 to 30 minutes, then scrub with stiff brush and hot water. Rinse with clean water.
5. Dissolve a cup tri-sodium phosphate in 1 gallon of hot water. Pour over stained cement surface generously and allow to soak 15 to 20 minutes. Scrub vigorously with stiff brush or broom. Rinse off with hose. Repeat if necessary.
6. Scrub the concrete with a grease solvent to remove as much as possible of the grease stain. Have good ventilation and avoid spark or flame as solvents are flammable. Naptha, often recommended, can ignite, just from a spark from friction or rubbing.
7. Mix 1 part sodium citrate to 6 parts water and 6 parts glycerin and add enough whiting or fuller's earth to make a thick paste. Spread paste on oil or grease stain. Let stand 1 week. Add new paste when it dries. Flush with water after brushing dry paste away. Repeat if necessary.

Rust Stains : Make a paste of 1 part sodium citrate crystals to 6 parts water and enough whiting or fuller's earth to make a paste. Spread paste on rust stains and allow to dry. Scrape off. Rust should be removed. Repeat if necessary.

I don't know what your floors are sealed with, but we used vinegar and water to mop with. For regular cleaning though, we just used a vaccuum with a "bare floor" setting. I think that once the "grout-lines" are cleaned out, that you would be able to keep them clean just by vaccuuming regularly. Perhaps a grout brush would be helpful in cleaning out the cracks?

Not sure what you mean by "spots, grease, scum" that won't come up with mopping - do you think that the concrete might have been been dirty before they sealed it? If so, they're there for good. If it's on top of the sealer, it should come off with 409 or some other general purpose cleanser.