To walk or progress with a slow heavy pace; plod: slog across the swamp; slogged through both volumes.
To work diligently for long hours: slogged away at Latin.
To make (one's way) with a slow heavy pace against resistance.
To strike with heavy blows.
A long exhausting march or hike: a slog through miles of jungle.
A long session of hard work: an 18-hour slog in the hay fields.