Let A = −(∇ − i~a)

2 + V be a magnetic Schr¨odinger operator acting on L

2

(R

n

), n ≥ 1,

where ~a = (a1, · · · , an) ∈ L

2

loc and 0 ≤ V ∈ L

1

loc. By means of area integral function, a

Hardy space H1

A associated with A can be defined. We then show that Riesz transforms

Tk = ( ∂

∂xk

− iak)A−1/2 associated with A, k = 1, · · · , n, are bounded from the Hardy

space H1

A into L

1

. By interpolation, the Riesz transforms Tk are bounded on L

p

for all

1 < p ≤ 2. We will also show that when a function b ∈ BMO(R

n

), the commutators

with the Riesz transforms [b, Tk](u) = Tk(bu) − bTk(u) are bounded on L

p

spaces for all

1 < p ≤ 2. This is joint work with Lixin Yan and El Maati Ouhabaz.