diff --git a/README.md b/README.md
index 1e75567d..f759843a 100644
--- a/README.md
+++ b/README.md
@@ -16,6 +16,23 @@ def main() -> int:
     return 0
 ```
 
+Jou has classes. They can have methods, but that's about it:
+otherwise Jou classes are just like structs in C.
+
+```python
+import "stdlib/io.jou"
+
+class Greeting:
+    target: byte*
+
+    def show(self) -> None:
+        printf("Hello %s\n", self->target)
+
+def main() -> int:
+    g = Greeting{target="World"}
+    g.show()    # Output: Hello World
+```
+
 See the [examples](./examples/) and [tests](./tests/) directories for more example programs
 or read [the Jou tutorial](./doc/tutorial.md).
 
diff --git a/doc/classes.md b/doc/classes.md
new file mode 100644
index 00000000..e5ae04a1
--- /dev/null
+++ b/doc/classes.md
@@ -0,0 +1,292 @@
+# Classes
+
+TL;DR:
+
+```python
+import "stdlib/io.jou"
+
+class Person:
+    name: byte*
+
+    def greet(self) -> None:
+        printf("Hello %s\n", self->name)   # self is a pointer (Person*)
+
+def main() -> int:
+    instance = Person{name="world"}
+    instance.greet()   # Output: Hello world
+    return 0
+```
+
+
+## Fields
+
+An instance of a Jou class is a chunk of memory that is large enough to store multiple values.
+For example, the following class has two integers:
+
+```python
+class Point:
+    x: int
+    y: int
+```
+
+Now every instance of `Point` will be at least 64 bits in size:
+32 bits for `x`, and 32 bits for `y`.
+In reality, instances may be bigger than expected due to
+[padding](https://stackoverflow.com/questions/4306186/structure-padding-and-packing),
+but this can be almost always ignored.
+
+You can use e.g. `Point{x=12, y=34}` to instantiate the class,
+and the usual `.` syntax to access its fields:
+
+```python
+import "stdlib/io.jou"
+
+class Point:
+    x: int
+    y: int
+
+def main() -> int:
+    p = Point{x=12, y=34}
+    printf("%d, %d\n", p.x, p.y)  # Output: 12, 34
+    p.y++
+    printf("%d, %d\n", p.x, p.y)  # Output: 12, 35
+    return 0
+```
+
+This does not allocate any heap memory (TODO: document heap allocations).
+In fact, it's basically same as creating two variables `x` and `y` in the `main()` function:
+
+```python
+import "stdlib/io.jou"
+
+def main() -> int:
+    x = 12
+    y = 34
+    printf("%d, %d\n", x, y)  # Output: 12, 34
+    return 0
+```
+
+This means that if you pass an instance of a class to a function, you get a copy,
+as if you had just passed the two integers:
+
+```python
+import "stdlib/io.jou"
+
+class Point:
+    x: int
+    y: int
+
+def increment_y(instance: Point) -> None:
+    instance.y++  # Doesn't work as expected
+
+def main() -> int:
+    p = Point{x = 12, y = 34}
+    increment_y(p)
+    printf("%d\n", p.y)  # Output: 34
+    return 0
+```
+
+For this reason, instances of classes are often passed around as [pointers](tutorial.md#pointers).
+This way the `increment_y()` function knows where the original instance is in the computer's memory,
+so that it can place the new value there instead of its own copy of the instance.
+Like this:
+
+```python
+import "stdlib/io.jou"
+
+class Point:
+    x: int
+    y: int
+
+def increment_y(ptr: Point*) -> None:
+    ptr->y++
+
+def main() -> int:
+    p = Point{x = 12, y = 34}
+    increment_y(&p)
+    printf("%d\n", p.y)  # Output: 35
+    return 0
+```
+
+Here `ptr->y` does the same thing as `(*ptr).y`:
+it accesses the `y` member of the instance located wherever the pointer `ptr` is pointing.
+
+
+## Methods
+
+The above `increment_y()` function does something with a point,
+so instead of a function, it would be better to write it as a method in the `Point` class:
+
+```python
+import "stdlib/io.jou"
+
+class Point:
+    x: int
+    y: int
+
+    def increment_y(self) -> None:
+        self->y++
+
+def main() -> int:
+    p = Point{x=12, y=34}
+    p.increment_y()
+    printf("%d\n", p.y)  # Output: 35
+    return 0
+```
+
+By default, methods take the instance as a pointer.
+In the above example, the type of `self` is `Point*`,
+which means that `self` is a pointer to an instance of `Point`.
+
+To call a method on a pointer (such as `self`),
+use `->`, just like with accessing fields:
+
+```python
+import "stdlib/io.jou"
+
+class Point:
+    x: int
+    y: int
+
+    def increment_x(self) -> None:
+        self->x++
+
+    def increment_y(self) -> None:
+        self->y++
+
+    def increment_both(self) -> None:
+        self->increment_x()
+        self->increment_y()
+
+def main() -> int:
+    p = Point{x=12, y=34}
+    p.increment_both()
+    printf("%d %d\n", p.x, p.y)  # Output: 13 35
+    return 0
+```
+
+If, for some reason, you want to pass the instance by value instead of a pointer,
+so that the method gets a copy of it,
+you can specify the type of `self` like this:
+
+```python
+class Point:
+    def do_something(self: Point) -> None:
+        ...
+```
+
+This means that the type of `self` is `Point`, not `Point*` (the default),
+so `self` is not a pointer.
+
+
+## Instantiating
+
+As we have seen, the instantiating syntax is `ClassName{field=value}`.
+The curly braces are used to distinguish instantiating from function calls.
+
+If you omit some class fields, they will be initialized to zero.
+Specifically, the memory used for the fields will be all zero bytes.
+This means that boolean fields are set to `False`,
+numbers are set to zero,
+pointer fields become `NULL`,
+and fixed size strings appear as empty:
+
+```python
+import "stdlib/io.jou"
+
+
+class Person:
+    name: byte*
+    country: byte[50]
+
+    def introduce(self) -> None:
+        if self->name == NULL:
+            printf("I'm an anonymous person from '%s'\n", self->country)
+        else:
+            printf("I'm %s from '%s'\n", self->name, self->country)
+
+
+def main() -> int:
+    akuli = Person{name="Akuli", country="Finland"}
+    akuli.introduce()  # Output: I'm Akuli from 'Finland'
+
+    akuli = Person{name="Akuli"}
+    akuli.introduce()  # Output: I'm Akuli from ''
+
+    akuli = Person{}
+    akuli.introduce()  # Output: I'm an anonymous person from ''
+
+    return 0
+```
+
+You can achieve the same thing by setting the memory used by the instance to zero bytes.
+This is often done with the `memset()` function from [stdlib/mem.jou](../stdlib/mem.jou).
+It takes in three parameters, so that `memset(ptr, 0, n)` sets `n` bytes starting at pointer `ptr` to zero.
+To calculate the correct `n`, you can use the `sizeof` operator (TODO: document sizeof):
+
+```python
+import "stdlib/io.jou"
+import "stdlib/mem.jou"
+
+
+class Person:
+    name: byte*
+    country: byte[50]
+
+    def introduce(self) -> None:
+        if self->name == NULL:
+            printf("I'm an anonymous person from '%s'\n", self->country)
+        else:
+            printf("I'm %s from '%s'\n", self->name, self->country)
+
+
+def main() -> int:
+    akuli = Person{name="Akuli", country="Finland"}
+    memset(&akuli, 0, sizeof(akuli))
+    akuli.introduce()  # Output: I'm an anonymous person from ''
+    return 0
+```
+
+This works the same way if you have multiple instances next to each other in memory,
+such as in an array, and you want to zero-initialize all of them:
+
+```python
+import "stdlib/io.jou"
+import "stdlib/mem.jou"
+
+class Person:
+    name: byte*
+    country: byte[50]
+
+    def introduce(self) -> None:
+        if self->name == NULL:
+            printf("I'm an anonymous person from '%s'\n", self->country)
+        else:
+            printf("I'm %s from '%s'\n", self->name, self->country)
+
+def main() -> int:
+    contributors = [
+        Person{name="Akuli", country="Finland"},
+        Person{name="littlewhitecloud", country="China"},
+        Person{name="Moosems", country="USA"},
+    ]
+
+    # Output: I'm Akuli from 'Finland'
+    # Output: I'm littlewhitecloud from 'China'
+    # Output: I'm Moosems from 'USA'
+    for i = 0; i < 3; i++:
+        contributors[i].introduce()
+
+    memset(&contributors, 0, sizeof(contributors))
+
+    # Output: I'm an anonymous person from ''
+    # Output: I'm an anonymous person from ''
+    # Output: I'm an anonymous person from ''
+    for i = 0; i < 3; i++:
+        contributors[i].introduce()
+
+    return 0
+```
+
+Here `sizeof(contributors)` is the size of the entire array in bytes,
+which is 3 times the size of a `Person`.
diff --git a/doctest.sh b/doctest.sh
index 46fad451..17ff9e21 100755
--- a/doctest.sh
+++ b/doctest.sh
@@ -1,18 +1,18 @@
 #!/usr/bin/env bash
 #
-# This file runs code snippets in doc/*.md files.
+# This file runs code snippets in markdown files.
 
 set -e -o pipefail
 
 for arg in "$@"; do
     if [[ "$arg" =~ ^- ]]; then
-        echo "Usage: $0 [doc/file1.md doc/file2.md ...]" >&2
+        echo "Usage: $0 [file1.md file2.md ...]" >&2
         exit 2
     fi
 done
 
 if [ $# == 0 ]; then
-    files=(doc/*.md)
+    files=(README.md doc/*.md)
 else
     files=("$@")
 fi