A turbine airfoil (10) includes an impingement structure (26A, 26B) comprising a hollow elongated main body (28) positioned in an interior portion (11) of an airfoil body (12). The main body (28) extends lengthwise along a radial direction and defines coolant cavity (64) therewithin that receives a cooling fluid (60). The main body (28) is spaced from a pressure side wall (16) and a suction side wall (18) of the airfoil body (12) and may be spaced from an airfoil tip (52), to define respective passages (72, 74, 77) therebetween. A plurality of impingement openings (25) are formed through the main body (28) that connect the coolant cavity (64) with one or more of the respective passages (72, 74, 77). The impingement openings (25) direct the cooling fluid (60) flowing in the coolant cavity (64) to impinge on the pressure and/or suction side walls (16, 18) and/or the airfoil tip (52).