diff --git a/examples/arithmetics.rs b/examples/arithmetics.rs
new file mode 100644
index 00000000000..3123b951521
--- /dev/null
+++ b/examples/arithmetics.rs
@@ -0,0 +1,84 @@
+use arrow2::array::{Array, PrimitiveArray};
+use arrow2::compute::arithmetics::*;
+use arrow2::compute::arity::{binary, unary};
+use arrow2::datatypes::DataType;
+use arrow2::error::Result;
+
+fn main() -> Result<()> {
+    // say we have two arrays
+    let array0 = PrimitiveArray::<i64>::from(&[Some(1), Some(2), Some(3)]);
+    let array1 = PrimitiveArray::<i64>::from(&[Some(4), None, Some(6)]);
+
+    // we can add them as follows:
+    let added = arithmetic_primitive(&array0, Operator::Add, &array1)?;
+    assert_eq!(
+        added,
+        PrimitiveArray::<i64>::from(&[Some(5), None, Some(9)])
+    );
+
+    // subtract:
+    let subtracted = arithmetic_primitive(&array0, Operator::Subtract, &array1)?;
+    assert_eq!(
+        subtracted,
+        PrimitiveArray::<i64>::from(&[Some(-3), None, Some(-3)])
+    );
+
+    // add a scalar:
+    let plus10 = arithmetic_primitive_scalar(&array0, Operator::Add, &10)?;
+    assert_eq!(
+        plus10,
+        PrimitiveArray::<i64>::from(&[Some(11), Some(12), Some(13)])
+    );
+
+    // when the array is a trait object, there is a similar API
+    let array0 = &array0 as &dyn Array;
+    let array1 = &array1 as &dyn Array;
+
+    // check whether the logical types support addition (they could be any `Array`).
+    assert!(can_arithmetic(
+        array0.data_type(),
+        Operator::Add,
+        array1.data_type()
+    ));
+
+    // add them
+    let added = arithmetic(array0, Operator::Add, array1).unwrap();
+    assert_eq!(
+        PrimitiveArray::<i64>::from(&[Some(5), None, Some(9)]),
+        added.as_ref(),
+    );
+
+    // a more exotic implementation: arbitrary binary operations
+    // this is compiled to SIMD when intrinsics exist.
+    let array0 = PrimitiveArray::<i64>::from(&[Some(1), Some(2), Some(3)]);
+    let array1 = PrimitiveArray::<i64>::from(&[Some(4), None, Some(6)]);
+
+    let op = |x: i64, y: i64| x.pow(2) + y.pow(2);
+    let r = binary(&array0, &array1, DataType::Int64, op)?;
+    assert_eq!(
+        r,
+        PrimitiveArray::<i64>::from(&[Some(1 + 16), None, Some(9 + 36)])
+    );
+
+    // arbitrary unary operations
+    // this is compiled to SIMD when intrinsics exist.
+    let array0 = PrimitiveArray::<f64>::from(&[Some(4.0), None, Some(6.0)]);
+    let r = unary(
+        &array0,
+        |x| x.cos().powi(2) + x.sin().powi(2),
+        DataType::Float64,
+    );
+    assert!((r.values()[0] - 1.0).abs() < 0.0001);
+    assert!(r.is_null(1));
+    assert!((r.values()[2] - 1.0).abs() < 0.0001);
+
+    // finally, a transformation that changes types:
+    let array0 = PrimitiveArray::<f64>::from(&[Some(4.4), None, Some(4.6)]);
+    let rounded = unary(&array0, |x| x.round() as i64, DataType::Int64);
+    assert_eq!(
+        rounded,
+        PrimitiveArray::<i64>::from(&[Some(4), None, Some(5)])
+    );
+
+    Ok(())
+}
diff --git a/guide/src/SUMMARY.md b/guide/src/SUMMARY.md
index a73ef112ecd..cdf5aec37ee 100644
--- a/guide/src/SUMMARY.md
+++ b/guide/src/SUMMARY.md
@@ -4,6 +4,7 @@
 - [The arrow format](./arrow.md)
 - [Low-level API](./low_level.md)
 - [High-level API](./high_level.md)
+- [Compute](./compute.md)
 - [Metadata](./metadata.md)
 - [Foreign interfaces](./ffi.md)
 - [IO](./io/README.md)
diff --git a/guide/src/compute.md b/guide/src/compute.md
new file mode 100644
index 00000000000..68948149de0
--- /dev/null
+++ b/guide/src/compute.md
@@ -0,0 +1,23 @@
+# Compute API
+
+When compiled with the feature `compute`, this crate offers a wide range of functions to perform both vertical (e.g. add two arrays) and horizontal (compute the sum of an array) operations.
+
+```rust
+{{#include ../../examples/arithmetics.rs}}
+```
+
+An overview of the implemented functionality.
+
+* arithmetics, checked, saturating, etc.
+* `sum`, `min` and `max`
+* `unary`, `binary`, etc.
+* `comparison`
+* `cast`
+* `take`, `filter`, `concat`
+* `sort`, `hash`, `merge-sort`
+* `if-then-else`
+* `nullif`
+* `lenght` (of string)
+* `hour`, `year` (of temporal logical types)
+* `regex`
+* (list) `contains`
diff --git a/src/compute/arithmetics/mod.rs b/src/compute/arithmetics/mod.rs
index ce21ed3c140..496f02d72f3 100644
--- a/src/compute/arithmetics/mod.rs
+++ b/src/compute/arithmetics/mod.rs
@@ -228,7 +228,8 @@ pub enum Operator {
 }
 
 /// Perform arithmetic operations on two primitive arrays based on the Operator enum
-fn arithmetic_primitive<T>(
+//
+pub fn arithmetic_primitive<T>(
     lhs: &PrimitiveArray<T>,
     op: Operator,
     rhs: &PrimitiveArray<T>,
diff --git a/src/compute/arity.rs b/src/compute/arity.rs
index 0e99c488e16..e69d8162a21 100644
--- a/src/compute/arity.rs
+++ b/src/compute/arity.rs
@@ -128,7 +128,8 @@ where
 /// Applies a binary operations to two primitive arrays. This is the fastest
 /// way to perform an operation on two primitive array when the benefits of a
 /// vectorized operation outweighs the cost of branching nulls and non-nulls.
-///
+/// # Errors
+/// This function errors iff the arrays have a different length.
 /// # Implementation
 /// This will apply the function for all values, including those on null slots.
 /// This implies that the operation must be infallible for any value of the