diff --git a/forge_core/src/ast.rs b/forge_core/src/ast.rs
index 1e55f99..1ce8eaa 100644
--- a/forge_core/src/ast.rs
+++ b/forge_core/src/ast.rs
@@ -135,6 +135,19 @@ pub enum Operator {
     Mul,
     Div,
     Mod,
+    And,
+    Or,
+    BitAnd,
+    BitOr,
+    Xor,
+    Lt,
+    Le,
+    Gt,
+    Ge,
+    Eq,
+    Ne,
+    Lshift,
+    Rshift,
 }
 
 #[derive(PartialEq, Clone, Debug)]
diff --git a/forge_core/src/forge.pest b/forge_core/src/forge.pest
index 2cd78d5..5da8603 100644
--- a/forge_core/src/forge.pest
+++ b/forge_core/src/forge.pest
@@ -25,8 +25,28 @@ sub = { "-" }
 mul = { "*" }
 div = { "/" }
 modulus = { "%" }
+log_and = { "&&" }
+log_or = { "||" }
+bit_and = { "&" }
+bit_or = { "|" }
+xor = { "^" }
+lt = { "<" }
+le = { "<=" }
+gt = { ">" }
+ge = { ">=" }
+eq = { "==" }
+ne = { "!=" }
+lshift = { "<<" }
+rshift = { ">>" }
 
-operator = _{ add | sub | mul | div | modulus }
+operator = _{
+ add | sub |
+ mul | div | modulus |
+ log_and | log_or |
+ bit_and | bit_or | xor |
+ lshift | rshift |
+ lt | le | gt | ge |
+ eq | ne }
 expr = { val ~ (operator ~ val)* }
 val = { // These are what get evaluated and left on the stack:
   number | // Literal numbers
diff --git a/forge_core/src/forge_parser.rs b/forge_core/src/forge_parser.rs
index a83434e..2061a88 100644
--- a/forge_core/src/forge_parser.rs
+++ b/forge_core/src/forge_parser.rs
@@ -12,6 +12,14 @@ lazy_static::lazy_static! {
 
         // Precedence is defined lowest to highest
         PrattParser::new()
+            .op(Op::infix(log_or, Left))
+            .op(Op::infix(log_and, Left))
+            .op(Op::infix(bit_or, Left))
+            .op(Op::infix(xor, Left))
+            .op(Op::infix(bit_and, Left))
+            .op(Op::infix(eq, Left) | Op::infix(ne, Left))
+            .op(Op::infix(gt, Left) | Op::infix(ge, Left) | Op::infix(lt, Left) | Op::infix(le, Left))
+            .op(Op::infix(lshift, Left) | Op::infix(rshift, Left))
             .op(Op::infix(add, Left) | Op::infix(sub, Left))
             .op(Op::infix(mul, Left) | Op::infix(div, Left) | Op::infix(modulus, Left))
     };
@@ -475,6 +483,19 @@ impl AstNode for Operator {
             "*" => Self::Mul,
             "/" => Self::Div,
             "%" => Self::Mod,
+            "&&" => Self::And,
+            "||" => Self::Or,
+            "&" => Self::BitAnd,
+            "|" => Self::BitOr,
+            "^" => Self::Xor,
+            ">" => Self::Gt,
+            ">=" => Self::Ge,
+            "<" => Self::Lt,
+            "<=" => Self::Le,
+            "==" => Self::Eq,
+            "!=" => Self::Ne,
+            "<<" => Self::Lshift,
+            ">>" => Self::Rshift,
             _ => unreachable!(),
         }
     }
@@ -744,6 +765,40 @@ mod test {
             Ok(Expr(Expr(2.into(), Mul, 3.into()).into(), Add, 4.into()))
         );
 
+        assert_eq!(
+            Node::from_str("1 || 2 && 3"),
+            Ok(Expr(1.into(), Or, Expr(2.into(), And, 3.into()).into()))
+        );
+
+        assert_eq!(
+            Node::from_str("2 && &blah"),
+            Ok(Expr(2.into(), And, Address("blah".into()).into()))
+        );
+
+        assert_eq!(
+            Node::from_str("2 & &blah"),
+            Ok(Expr(2.into(), BitAnd, Address("blah".into()).into()))
+        );
+
+        assert_eq!(
+            Node::from_str("1 | 2 ^ 3"),
+            Ok(Expr(1.into(), BitOr, Expr(2.into(), Xor, 3.into()).into()))
+        );
+
+        assert_eq!(
+            Node::from_str("x == y > z"),
+            Ok(Expr(
+                Name("x".into()).into(),
+                Eq,
+                Expr(Name("y".into()).into(), Gt, Name("z".into()).into()).into()
+            ))
+        );
+
+        assert_eq!(
+            Node::from_str("1 << 6"),
+            Ok(Expr(1.into(), Lshift, 6.into()))
+        );
+
         // Parens
         assert_eq!(
             Node::from_str("(1 + 2) * 3"),