diff --git a/.github/workflows/rust.yml b/.github/workflows/rust.yml
index 2ea4a7fa9..146a97269 100644
--- a/.github/workflows/rust.yml
+++ b/.github/workflows/rust.yml
@@ -41,6 +41,63 @@ jobs:
             $(find ./target/debug -type f -perm -100 | grep gimli | head -n 1) \
             > /dev/null
 
+  build_fuzz_targets:
+    name: Build fuzz targets
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v2
+      - name: Install rustup
+        run: curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh -s -- -y --profile=minimal
+      - name: Install nightly rust
+        run: |
+          rustup install nightly
+          rustup default nightly
+      - name: Install `cargo fuzz`
+        run: cargo install cargo-fuzz --vers "^0.7.4"
+      - run: cargo fuzz build -Oa
+      - uses: actions/upload-artifact@v2
+        with:
+          name: fuzz-targets
+          path: fuzz/target/x86_64-unknown-linux-gnu/release/debug_*
+      - uses: actions/upload-artifact@v2
+        with:
+          name: fuzz-targets
+          path: fuzz/target/x86_64-unknown-linux-gnu/release/eh_*
+
+  run_fuzz_targets:
+    strategy:
+      matrix:
+        fuzz_target: ["debug_abbrev", "debug_aranges", "debug_info", "debug_line", "eh_frame", "eh_frame_hdr"]
+    name: "Run `${{matrix.fuzz_target}}` fuzz target"
+    needs: build_fuzz_targets
+    runs-on: ubuntu-latest
+    steps:
+      - name: Clone the fuzz corpora
+        uses: actions/checkout@v2
+        with:
+          repository: gimli-rs/gimli-libfuzzer-corpora
+          path: corpora
+      - name: Download fuzz targets
+        uses: actions/download-artifact@v1
+        with:
+          name: fuzz-targets
+        # Note: -max_total_time=300 == 300 seconds == 5 minutes.
+      - name: "Run `${{matrix.fuzz_target}}` fuzz target"
+        run: |
+          mkdir ${{matrix.fuzz_target}}_artifacts
+          chmod +x ./fuzz-targets/${{matrix.fuzz_target}}
+          ./fuzz-targets/${{matrix.fuzz_target}} ./corpora/${{matrix.fuzz_target}} \
+              -max_total_time=300 \
+              -artifact_prefix=./${{matrix.fuzz_target}}_artifacts/
+      # If fuzzing finds a new crash/panic/etc, upload the input artifacts so we
+      # can debug them.
+      - name: Upload fuzz artifacts
+        if: failure()
+        uses: actions/upload-artifact@v2
+        with:
+          name: ${{matrix.fuzz_target}}_artifacts
+          path: ./${{matrix.fuzz_target}}_artifacts
+
   features:
     runs-on: ubuntu-latest
     steps:
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index d30c77b2e..4f9e574ce 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -9,6 +9,7 @@ out to us in a GitHub issue, or ping `fitzgen` in `#rust` on `irc.mozilla.org`.
 * [Testing `gimli`](#testing)
   * [Test Coverage](#coverage)
   * [Using `test-assembler`](#test-assembler)
+  * [Fuzzing](#fuzzing)
 * [Benchmarking](#benchmarking)
 * [Style](#style)
 
@@ -81,6 +82,27 @@ construct binary test data. It makes building complex test cases readable.
 
 [Here is an example usage in `gimli`](https://github.com/gimli-rs/gimli/blob/156451f3fe6eeb2fa62b84b362c33fcb176e1171/src/loc.rs#L263)
 
+### <a id="fuzzing"></a> Fuzzing
+
+First, install `cargo fuzz`:
+
+```
+$ cargo install cargo-fuzz
+```
+
+Optionally, [set up the corpora for our fuzz targets by following these
+instructions](https://github.com/gimli-rs/gimli-libfuzzer-corpora/blob/master/README.md#using-these-corpora).
+
+Finally, run a fuzz target! In this case, we are running the `eh_frame` fuzz
+target:
+
+```
+$ cargo fuzz run eh_frame
+```
+
+The fuzz target definitions live in `fuzz/fuzz_targets/*`. You can add new ones
+via `cargo fuzz add <my_new_target>`.
+
 ## <a id="benchmarking"></a> Benchmarking
 
 The benchmarks require nightly `rustc`, so use `rustup`:
diff --git a/fixtures/self/eh_frame_hdr b/fixtures/self/eh_frame_hdr
new file mode 100644
index 000000000..a590ba213
Binary files /dev/null and b/fixtures/self/eh_frame_hdr differ
diff --git a/fuzz/.gitignore b/fuzz/.gitignore
new file mode 100644
index 000000000..572e03bdf
--- /dev/null
+++ b/fuzz/.gitignore
@@ -0,0 +1,4 @@
+
+target
+corpus
+artifacts
diff --git a/fuzz/Cargo.toml b/fuzz/Cargo.toml
new file mode 100644
index 000000000..b9f3ca29a
--- /dev/null
+++ b/fuzz/Cargo.toml
@@ -0,0 +1,44 @@
+
+[package]
+name = "gimli-fuzz"
+version = "0.0.0"
+authors = ["Automatically generated"]
+publish = false
+edition = "2018"
+
+[package.metadata]
+cargo-fuzz = true
+
+[dependencies]
+libfuzzer-sys = "0.3"
+
+[dependencies.gimli]
+path = ".."
+
+# Prevent this from interfering with workspaces
+[workspace]
+members = ["."]
+
+[[bin]]
+name = "debug_info"
+path = "fuzz_targets/debug_info.rs"
+
+[[bin]]
+name = "debug_abbrev"
+path = "fuzz_targets/debug_abbrev.rs"
+
+[[bin]]
+name = "debug_line"
+path = "fuzz_targets/debug_line.rs"
+
+[[bin]]
+name = "eh_frame"
+path = "fuzz_targets/eh_frame.rs"
+
+[[bin]]
+name = "debug_aranges"
+path = "fuzz_targets/debug_aranges.rs"
+
+[[bin]]
+name = "eh_frame_hdr"
+path = "fuzz_targets/eh_frame_hdr.rs"
diff --git a/fuzz/fuzz_targets/debug_abbrev.rs b/fuzz/fuzz_targets/debug_abbrev.rs
new file mode 100755
index 000000000..26484a2f2
--- /dev/null
+++ b/fuzz/fuzz_targets/debug_abbrev.rs
@@ -0,0 +1,16 @@
+#![no_main]
+
+use gimli::{read::DebugAbbrev, DebugAbbrevOffset, LittleEndian};
+use libfuzzer_sys::fuzz_target;
+
+fuzz_target!(|debug_abbrev: &[u8]| {
+    let len = debug_abbrev.len();
+    let debug_abbrev = DebugAbbrev::new(&debug_abbrev, LittleEndian);
+
+    let offset = DebugAbbrevOffset(0);
+    if let Ok(abbreviations) = debug_abbrev.abbreviations(offset) {
+        for i in 1..len {
+            let _ = abbreviations.get(i as u64);
+        }
+    }
+});
diff --git a/fuzz/fuzz_targets/debug_aranges.rs b/fuzz/fuzz_targets/debug_aranges.rs
new file mode 100755
index 000000000..a7484af79
--- /dev/null
+++ b/fuzz/fuzz_targets/debug_aranges.rs
@@ -0,0 +1,12 @@
+#![no_main]
+
+use gimli::{read::DebugAranges, LittleEndian};
+use libfuzzer_sys::fuzz_target;
+
+fuzz_target!(|debug_aranges: &[u8]| {
+    let debug_aranges = DebugAranges::new(&debug_aranges, LittleEndian);
+    let mut items = debug_aranges.items();
+    while let Ok(Some(_entry)) = items.next() {
+        continue;
+    }
+});
diff --git a/fuzz/fuzz_targets/debug_info.rs b/fuzz/fuzz_targets/debug_info.rs
new file mode 100644
index 000000000..8cad4483b
--- /dev/null
+++ b/fuzz/fuzz_targets/debug_info.rs
@@ -0,0 +1,26 @@
+#![no_main]
+
+use gimli::{
+    read::{DebugAbbrev, DebugInfo},
+    LittleEndian,
+};
+use libfuzzer_sys::fuzz_target;
+
+fuzz_target!(|sections: (Vec<u8>, Vec<u8>)| {
+    let (debug_abbrev, debug_info) = sections;
+    let debug_abbrev = DebugAbbrev::new(&debug_abbrev, LittleEndian);
+    let debug_info = DebugInfo::new(&debug_info, LittleEndian);
+
+    let mut units = debug_info.units();
+    while let Ok(Some(unit)) = units.next() {
+        if let Ok(abbrevs) = unit.abbreviations(&debug_abbrev) {
+            let mut cursor = unit.entries(&abbrevs);
+            while let Ok(Some((_delta, entry))) = cursor.next_dfs() {
+                let mut attrs = entry.attrs();
+                while let Ok(Some(_attr)) = attrs.next() {
+                    continue;
+                }
+            }
+        }
+    }
+});
diff --git a/fuzz/fuzz_targets/debug_line.rs b/fuzz/fuzz_targets/debug_line.rs
new file mode 100755
index 000000000..c15cb45b9
--- /dev/null
+++ b/fuzz/fuzz_targets/debug_line.rs
@@ -0,0 +1,17 @@
+#![no_main]
+
+use gimli::{read::DebugLine, DebugLineOffset, LittleEndian};
+use libfuzzer_sys::fuzz_target;
+
+fuzz_target!(|debug_line: &[u8]| {
+    let debug_line = DebugLine::new(&debug_line, LittleEndian);
+
+    let offset = DebugLineOffset(0);
+    let address_size = 8;
+    if let Ok(program) = debug_line.program(offset, address_size, None, None) {
+        let mut rows = program.rows();
+        while let Ok(Some(row)) = rows.next_row() {
+            let _ = row;
+        }
+    }
+});
diff --git a/fuzz/fuzz_targets/eh_frame.rs b/fuzz/fuzz_targets/eh_frame.rs
new file mode 100755
index 000000000..ab44bd0c1
--- /dev/null
+++ b/fuzz/fuzz_targets/eh_frame.rs
@@ -0,0 +1,34 @@
+#![no_main]
+
+use gimli::{
+    read::{BaseAddresses, CieOrFde, EhFrame, UninitializedUnwindContext, UnwindSection},
+    LittleEndian,
+};
+use libfuzzer_sys::fuzz_target;
+
+fuzz_target!(|eh_frame: &[u8]| {
+    let eh_frame = EhFrame::new(&eh_frame, LittleEndian);
+
+    let mut ctx = UninitializedUnwindContext::new();
+    let bases = BaseAddresses::default()
+        .set_eh_frame(0)
+        .set_eh_frame_hdr(0)
+        .set_text(0)
+        .set_got(0);
+
+    let mut entries = eh_frame.entries(&bases);
+    while let Ok(Some(entry)) = entries.next() {
+        match entry {
+            CieOrFde::Cie(_) => continue,
+            CieOrFde::Fde(partial) => {
+                if let Ok(fde) = partial.parse(EhFrame::cie_from_offset) {
+                    if let Ok(mut table) = fde.rows(&eh_frame, &bases, &mut ctx) {
+                        while let Ok(Some(_row)) = table.next_row() {
+                            continue;
+                        }
+                    }
+                }
+            }
+        };
+    }
+});
diff --git a/fuzz/fuzz_targets/eh_frame_hdr.rs b/fuzz/fuzz_targets/eh_frame_hdr.rs
new file mode 100755
index 000000000..beaf2fa31
--- /dev/null
+++ b/fuzz/fuzz_targets/eh_frame_hdr.rs
@@ -0,0 +1,15 @@
+#![no_main]
+
+use gimli::{read::EhFrameHdr, BaseAddresses, LittleEndian};
+use libfuzzer_sys::fuzz_target;
+
+fuzz_target!(|eh_frame_hdr: &[u8]| {
+    let eh_frame_hdr = EhFrameHdr::new(eh_frame_hdr, LittleEndian);
+    let bases = BaseAddresses::default()
+        .set_eh_frame(0)
+        .set_eh_frame_hdr(0)
+        .set_text(0)
+        .set_got(0);
+    let address_size = 8;
+    let _ = eh_frame_hdr.parse(&bases, address_size);
+});
diff --git a/tests/parse_self.rs b/tests/parse_self.rs
old mode 100644
new mode 100755
index 694511b41..524998368
--- a/tests/parse_self.rs
+++ b/tests/parse_self.rs
@@ -404,3 +404,24 @@ fn test_parse_self_eh_frame() {
         }
     }
 }
+
+#[test]
+fn test_parse_self_eh_frame_hdr() {
+    use gimli::{BaseAddresses, EhFrameHdr};
+
+    let eh_frame_hdr = read_section("eh_frame_hdr");
+    let eh_frame_hdr = EhFrameHdr::new(&eh_frame_hdr, LittleEndian);
+
+    let bases = BaseAddresses::default()
+        .set_eh_frame(0)
+        .set_eh_frame_hdr(0)
+        .set_text(0)
+        .set_got(0);
+
+    // `.eh_frame_hdr` was generated on a 64 bit machine.
+    let address_size = 8;
+
+    let _parsed_header = eh_frame_hdr
+        .parse(&bases, address_size)
+        .expect("we can parse the `.eh_frame_hdr` section OK");
+}