For some just entering this hobby the term "CleanUp Crew" may sound like we're hiring a janitorial service for our tanks.  In a very real sense, we are!
The Clean Up crews we buy consist of invertebrates such as cucumbers, shrimps & snails.  Bristle worms, copepods & other organisms that enter our tanks as hitchhikers in & on the rock & corals we buy also provide necessary cleaning.  Remember, bristle worms act just like earth worms do for a garden.  They are "good guys", just don't touch them because their bristles will sting.
Now let's talk about who the reef safe ones are, why they are a "must have" in our tanks, the important benefits/functions of each & how many we should have (note: these are approximate numbers +/-.  New setups need more to target & clean-up the inevitable algae after a cycle so these numbers (algae grazers especially) are more for the initial numbers needed)

Cucumbers:  Pictured up top - 2 Cukes in my 180g  :c)  Fantastic top sand cleaners, physically eating sand grains & producing clean sand waste.  They will travel next to the base of your rocks targeting areas where detritus collect and where we can't reach!  Mine are non-toxic!  Bewarned though, others sell super toxic species & when they die will kill your tank!
Recommended numbers:  1-2 /3 Ft - 2-3 /4 Ft - 3+ /6 Ft tank.
2 or more in a tank may give you babies!

Pictured here...baby Cucumbers born at AquaCorals!  :c)

Astrea snails: Thorough algae eaters.  Target your rock & glass surfaces.  Other "turbo" type snails aren't as thorough & can topple rocks when larger.  Only downside to Astreas is that they can't right themselves when toppled upside down.  You must right them up when fallen...then they'll go on their merry way.  :0)
Recommended numbers:  1 per gallon of tank

Nassarius snails: Fantastic scavengers! They eat detritus, uneaten fish food & waste and burrow in the top 1 inch of your substrate keeping it loose & clean. They will "pop" out of the sand when you feed!
Recommended numbers:  1 per gallon of tank

TONGA Nassarius snails: Just like their smaller cousins above the Tonga species are about 6 times larger and have a beautiful shell to boot!  1 per 5 gallons of tank.

Cerith snails: Bury within the top 1/2 inch of your sand bed helping to keep it from compacting.  These cool elongated shelled snails clean the algae off the individual grains of sand and base of rocks.  They are well known for being a great defense against a cyano bacteria (Red Slime) breakout.
Recommended numbers:  1 per gallon of tank

 Emerald Crabs:  The only CRAB I sell to put in the main tank!  Great hair algae eaters & scavengers.
Recommended numbers:  1-2 /3 Ft - 2-3 /4 Ft - 3+ /6 Ft tank.

 Peppermint Shrimp & Cleaner Shrimp: Both shrimp are great scavengers that will help take care of uneaten fish foods & other wastes.

"True" Peppermint Shrimp (Lysmata wurdemanni) can clean a rock free of aiptasia as well as scavenge

Bewarned!  There is another shrimp called a Peppermint & it's not reef safe IMO so be sure you know what you're buying!  You can rest easy as mine are totally reef safe!

Cleaner Shrimp:

Skunk Cleaner Shrimp and

 Fire Cleaner Shrimp - both provide parasitic cleaning & manicures for fish!
Recommended numbers:  Pairs in any size tanks are cool!  Pairs will spawn.  2 pairs same or different species in a 4ft+ tank.

NOT Recommended for your main tank!  Though many places sell the below as part of their clean-up crew, I do not as they have bad behaviors:
Hermit Crabs:   True carnivores (meat eaters) - will make expensive lunches out of your good snails!  They are also known to irritate & sometimes kill Feather Dusters & more!  Stick with the clean-up crew listed here & be safe!
White Sifting Starfish:   Though they "sift/bury" into the sand they are hunting & eating your good live fauna!  Use Nassarius Snails instead that don't have "bad behaviors"!

In a nutshell, cleanup crews take care of uneaten foods & fish waste, keep the sand supple so gasses can escape, keep the rock clear of nuisance algae, clean parasites off fish & their spawning provides a feeding treat for all!  Buy them all at once or add to your population until you reach the recommended numbers then just replace as you see them pass away.