A dropper bottle assembly, comprising: a dropper bottle (100; 200) for containing and dispensing a liquid, the bottle (100; 200) having a top wall (120a; 220a), an outer wall adjacent to the top wall (120a; 220a), and a first set of threads (125; 225); a tip insert (140; 240) comprising: an insert body (140d; 240e); a sharp piercing point (140a; 240a) at a lower end of the insert body (140d; 240e) for piercing the top wall (120a; 220a) of the bottle (100; 200) and for retaining the tip insert (140; 240) on the top wall (120a; 220a) of the bottle (100; 200) after piercing; a passage (140b; 240b) extending from a distal end of the sharp piercing point (140a; 240a), through the insert body (140d: 240e), to an opposing upper surface of the insert body (140d; 240e); and a dispensing tip (140c; 240c) at the insert body (140d; 240e) upper surface communicating with the passage (140b; 240b) for forming drops of the liquid from the bottle (100; 200); and an overcap (130; 230) having a second set of threads (135; 235) for engaging the first set of threads (125; 225) to draw the overcap (130; 230) down towards the bottle (100; 200), and an inner surface for mating with the insert body (140d; 240e) to guide the sharp piercing point (140a; 240a) to a predetermined position on the top wall (120a; 220a) of the bottle (100; 200) prior to piercing the top wall (120a; 220a) of the bottle (100; 200); wherein when the first and second sets of threads (125, 135; 225, 235) are engaged to draw the overcap (130; 230) down towards the bottle (100; 200), the sharp piercing point (140a; 240a) of the tip insert (140; 240) pierces the top wall (120a; 220a) of the bottle (100; 200); wherein the tip insert body (140d; 240e) has a lower surface (140d1; 240e1); wherein the sharp piercing point (140a; 240a) includes a flange (140a1; 240a1) substantially parallel to the tip insert body lower surface (140d1; 240e1), and a shaft (140a2; 240a2) having a length substantially the same as a thickness of the bottle top wall (120a; 220a), the shaft (140a2; 240a2) being disposed between the flange (140a1; 240a1) and the tip insert body lower surface (140d1; 240e1); and wherein the bottle top wall (120a; 220a) is captured between the flange (140a1; 240a1) and the tip insert body lower surface (140d1; 240e1) after piercing by the sharp piercing point (140a; 240a). a dropper bottle (100; 200) for containing and dispensing a liquid, the bottle (100; 200) having a top wall (120a; 220a), an outer wall adjacent to the top wall (120a; 220a), and a first set of threads (125; 225); a tip insert (140; 240) comprising: an insert body (140d; 240e); a sharp piercing point (140a; 240a) at a lower end of the insert body (140d; 240e) for piercing the top wall (120a; 220a) of the bottle (100; 200) and for retaining the tip insert (140; 240) on the top wall (120a; 220a) of the bottle (100; 200) after piercing; a passage (140b; 240b) extending from a distal end of the sharp piercing point (140a; 240a), through the insert body (140d: 240e), to an opposing upper surface of the insert body (140d; 240e); and a dispensing tip (140c; 240c) at the insert body (140d; 240e) upper surface communicating with the passage (140b; 240b) for forming drops of the liquid from the bottle (100; 200); and an insert body (140d; 240e); a sharp piercing point (140a; 240a) at a lower end of the insert body (140d; 240e) for piercing the top wall (120a; 220a) of the bottle (100; 200) and for retaining the tip insert (140; 240) on the top wall (120a; 220a) of the bottle (100; 200) after piercing; a passage (140b; 240b) extending from a distal end of the sharp piercing point (140a; 240a), through the insert body (140d: 240e), to an opposing upper surface of the insert body (140d; 240e); and a dispensing tip (140c; 240c) at the insert body (140d; 240e) upper surface communicating with the passage (140b; 240b) for forming drops of the liquid from the bottle (100; 200); and an overcap (130; 230) having a second set of threads (135; 235) for engaging the first set of threads (125; 225) to draw the overcap (130; 230) down towards the bottle (100; 200), and an inner surface for mating with the insert body (140d; 240e) to guide the sharp piercing point (140a; 240a) to a predetermined position on the top wall (120a; 220a) of the bottle (100; 200) prior to piercing the top wall (120a; 220a) of the bottle (100; 200); wherein when the first and second sets of threads (125, 135; 225, 235) are engaged to draw the overcap (130; 230) down towards the bottle (100; 200), the sharp piercing point (140a; 240a) of the tip insert (140; 240) pierces the top wall (120a; 220a) of the bottle (100; 200); wherein the tip insert body (140d; 240e) has a lower surface (140d1; 240e1); wherein the sharp piercing point (140a; 240a) includes a flange (140a1; 240a1) substantially parallel to the tip insert body lower surface (140d1; 240e1), and a shaft (140a2; 240a2) having a length substantially the same as a thickness of the bottle top wall (120a; 220a), the shaft (140a2; 240a2) being disposed between the flange (140a1; 240a1) and the tip insert body lower surface (140d1; 240e1); and wherein the bottle top wall (120a; 220a) is captured between the flange (140a1; 240a1) and the tip insert body lower surface (140d1; 240e1) after piercing by the sharp piercing point (140a; 240a).