diff --git a/ibis/backends/trino/registry.py b/ibis/backends/trino/registry.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import operator
 from functools import partial, reduce
 from typing import Literal
 
@@ -11,6 +12,7 @@
 
 import ibis
 import ibis.common.exceptions as com
+import ibis.expr.datatypes as dt
 import ibis.expr.operations as ops
 from ibis.backends.base.sql.alchemy.registry import (
     _literal as _alchemy_literal,
@@ -27,6 +29,7 @@
     varargs,
 )
 from ibis.backends.postgres.registry import _corr, _covar
+from ibis.backends.trino.datatypes import INTERVAL
 
 operation_registry = sqlalchemy_operation_registry.copy()
 operation_registry.update(sqlalchemy_window_functions_registry)
@@ -68,8 +71,19 @@ def _literal(t, op):
         return sa.literal(float(value), type_=DOUBLE())
     elif dtype.is_integer():
         return sa.literal(int(value), type_=t.get_sqla_type(dtype))
+    elif dtype.is_timestamp():
+        return sa.cast(
+            sa.func.from_iso8601_timestamp(value.isoformat()), t.get_sqla_type(dtype)
+        )
     elif dtype.is_date():
+        return sa.func.from_iso8601_date(value.isoformat())
+    elif dtype.is_time():
         return sa.cast(sa.literal(str(value)), t.get_sqla_type(dtype))
+    elif dtype.is_interval():
+        return sa.literal_column(
+            f"INTERVAL '{value}' {dtype.resolution.upper()}", type_=INTERVAL
+        )
+
     return _alchemy_literal(t, op)
 
 
@@ -324,6 +338,18 @@ def _array_intersect(t, op):
     3,
 )
 
+
+def _interval_from_integer(t, op):
+    unit = op.unit.short
+    if unit in ("Y", "Q", "M", "W"):
+        raise com.UnsupportedOperationError(f"Interval unit {unit!r} not supported")
+    arg = sa.func.concat(
+        t.translate(ops.Cast(op.arg, dt.String(nullable=op.arg.dtype.nullable))),
+        unit.lower(),
+    )
+    return sa.type_coerce(sa.func.parse_duration(arg), INTERVAL)
+
+
 operation_registry.update(
     {
         # conditional expressions
@@ -511,6 +537,15 @@ def _array_intersect(t, op):
         ops.TimeDelta: _temporal_delta,
         ops.DateDelta: _temporal_delta,
         ops.TimestampDelta: _temporal_delta,
+        ops.TimestampAdd: fixed_arity(operator.add, 2),
+        ops.TimestampSub: fixed_arity(operator.sub, 2),
+        ops.TimestampDiff: fixed_arity(lambda x, y: sa.type_coerce(x - y, INTERVAL), 2),
+        ops.DateAdd: fixed_arity(operator.add, 2),
+        ops.DateSub: fixed_arity(operator.sub, 2),
+        ops.DateDiff: fixed_arity(lambda x, y: sa.type_coerce(x - y, INTERVAL), 2),
+        ops.IntervalAdd: fixed_arity(operator.add, 2),
+        ops.IntervalSubtract: fixed_arity(operator.sub, 2),
+        ops.IntervalFromInteger: _interval_from_integer,
     }
 )