R has many *apply functions which are ably described in the help files (e.g. ?apply
). There are enough of them, though, that beginning useRs may have difficulty deciding which one is appropriate for their situation or even remembering them all. They may have a general sense that “I should be using an *apply function here”, but it can be tough to keep them all straight at first.
Despite the fact (noted in other answers) that much of the functionality of the *apply family is covered by the extremely popular plyr
package, the base functions remain useful and worth knowing.
This answer is intended to act as a sort of signpost for new useRs to help direct them to the correct *apply function for their particular problem. Note, this is not intended to simply regurgitate or replace the R documentation! The hope is that this answer helps you to decide which *apply function suits your situation and then it is up to you to research it further. With one exception, performance differences will not be addressed.

apply – When you want to apply a function to the rows or columns
of a matrix (and higherdimensional analogues); not generally advisable for data frames as it will coerce to a matrix first.# Two dimensional matrix M < matrix(seq(1,16), 4, 4) # apply min to rows apply(M, 1, min) [1] 1 2 3 4 # apply max to columns apply(M, 2, max) [1] 4 8 12 16 # 3 dimensional array M < array( seq(32), dim = c(4,4,2)) # Apply sum across each M[*, , ]  i.e Sum across 2nd and 3rd dimension apply(M, 1, sum) # Result is onedimensional [1] 120 128 136 144 # Apply sum across each M[*, *, ]  i.e Sum across 3rd dimension apply(M, c(1,2), sum) # Result is twodimensional [,1] [,2] [,3] [,4] [1,] 18 26 34 42 [2,] 20 28 36 44 [3,] 22 30 38 46 [4,] 24 32 40 48
If you want row/column means or sums for a 2D matrix, be sure to
investigate the highly optimized, lightningquickcolMeans
,
rowMeans
,colSums
,rowSums
. 
lapply – When you want to apply a function to each element of a
list in turn and get a list back.This is the workhorse of many of the other *apply functions. Peel
back their code and you will often findlapply
underneath.x < list(a = 1, b = 1:3, c = 10:100) lapply(x, FUN = length) $a [1] 1 $b [1] 3 $c [1] 91 lapply(x, FUN = sum) $a [1] 1 $b [1] 6 $c [1] 5005

sapply – When you want to apply a function to each element of a
list in turn, but you want a vector back, rather than a list.If you find yourself typing
unlist(lapply(...))
, stop and consider
sapply
.x < list(a = 1, b = 1:3, c = 10:100) # Compare with above; a named vector, not a list sapply(x, FUN = length) a b c 1 3 91 sapply(x, FUN = sum) a b c 1 6 5005
In more advanced uses of
sapply
it will attempt to coerce the
result to a multidimensional array, if appropriate. For example, if our function returns vectors of the same length,sapply
will use them as columns of a matrix:sapply(1:5,function(x) rnorm(3,x))
If our function returns a 2 dimensional matrix,
sapply
will do essentially the same thing, treating each returned matrix as a single long vector:sapply(1:5,function(x) matrix(x,2,2))
Unless we specify
simplify = "array"
, in which case it will use the individual matrices to build a multidimensional array:sapply(1:5,function(x) matrix(x,2,2), simplify = "array")
Each of these behaviors is of course contingent on our function returning vectors or matrices of the same length or dimension.

vapply – When you want to use
sapply
but perhaps need to
squeeze some more speed out of your code or want more type safety.For
vapply
, you basically give R an example of what sort of thing
your function will return, which can save some time coercing returned
values to fit in a single atomic vector.x < list(a = 1, b = 1:3, c = 10:100) #Note that since the advantage here is mainly speed, this # example is only for illustration. We're telling R that # everything returned by length() should be an integer of # length 1. vapply(x, FUN = length, FUN.VALUE = 0L) a b c 1 3 91

mapply – For when you have several data structures (e.g.
vectors, lists) and you want to apply a function to the 1st elements
of each, and then the 2nd elements of each, etc., coercing the result
to a vector/array as insapply
.This is multivariate in the sense that your function must accept
multiple arguments.#Sums the 1st elements, the 2nd elements, etc. mapply(sum, 1:5, 1:5, 1:5) [1] 3 6 9 12 15 #To do rep(1,4), rep(2,3), etc. mapply(rep, 1:4, 4:1) [[1]] [1] 1 1 1 1 [[2]] [1] 2 2 2 [[3]] [1] 3 3 [[4]] [1] 4

Map – A wrapper to
mapply
withSIMPLIFY = FALSE
, so it is guaranteed to return a list.Map(sum, 1:5, 1:5, 1:5) [[1]] [1] 3 [[2]] [1] 6 [[3]] [1] 9 [[4]] [1] 12 [[5]] [1] 15

rapply – For when you want to apply a function to each element of a nested list structure, recursively.
To give you some idea of how uncommon
rapply
is, I forgot about it when first posting this answer! Obviously, I’m sure many people use it, but YMMV.rapply
is best illustrated with a userdefined function to apply:# Append ! to string, otherwise increment myFun < function(x){ if(is.character(x)){ return(paste(x,"!",sep="")) } else{ return(x + 1) } } #A nested list structure l < list(a = list(a1 = "Boo", b1 = 2, c1 = "Eeek"), b = 3, c = "Yikes", d = list(a2 = 1, b2 = list(a3 = "Hey", b3 = 5))) # Result is named vector, coerced to character rapply(l, myFun) # Result is a nested list like l, with values altered rapply(l, myFun, how="replace")

tapply – For when you want to apply a function to subsets of a
vector and the subsets are defined by some other vector, usually a
factor.The black sheep of the *apply family, of sorts. The help file’s use of
the phrase “ragged array” can be a bit confusing, but it is actually
quite simple.A vector:
x < 1:20
A factor (of the same length!) defining groups:
y < factor(rep(letters[1:5], each = 4))
Add up the values in
x
within each subgroup defined byy
:tapply(x, y, sum) a b c d e 10 26 42 58 74
More complex examples can be handled where the subgroups are defined
by the unique combinations of a list of several factors.tapply
is
similar in spirit to the splitapplycombine functions that are
common in R (aggregate
,by
,ave
,ddply
, etc.) Hence its
black sheep status.