diff --git a/lib/rex.rb b/lib/rex.rb
index d46dd06..3460e1c 100644
--- a/lib/rex.rb
+++ b/lib/rex.rb
@@ -3,7 +3,9 @@
 require_relative "rex/version"
 require_relative "rex/limit"
 require_relative "rex/order"
+require_relative "rex/trade"
 require_relative "rex/order_book"
+require_relative "rex/matcher"
 
 module Rex
   class Error < StandardError; end
diff --git a/lib/rex/matcher.rb b/lib/rex/matcher.rb
new file mode 100644
index 0000000..1dc39ff
--- /dev/null
+++ b/lib/rex/matcher.rb
@@ -0,0 +1,40 @@
+module Rex
+  class Matcher
+    def match(order_book)
+      trades = []
+      highest_buy_order = order_book.highest_buy_order
+      lowest_sell_order = order_book.lowest_sell_order
+      return trades if highest_buy_order.nil? || lowest_sell_order.nil?
+
+      while highest_buy_order&.price&.>= lowest_sell_order&.price
+        max_amount = [highest_buy_order.remaining_amount, lowest_sell_order.remaining_amount].min
+        highest_buy_order.remaining_amount -= max_amount
+        lowest_sell_order.remaining_amount -= max_amount
+
+        trades << Trade.new(
+          id: order_book.next_trade_id,
+          buy_order: highest_buy_order,
+          sell_order: lowest_sell_order,
+          amount: max_amount,
+          price: lowest_sell_order.price
+        )
+
+        remove_if_filled(highest_buy_order, order_book)
+        remove_if_filled(lowest_sell_order, order_book)
+
+        # Go for the next run
+        highest_buy_order = order_book.highest_buy_order
+        lowest_sell_order = order_book.lowest_sell_order
+
+        return trades if highest_buy_order.nil? || lowest_sell_order.nil?
+      end
+    end
+
+    private
+
+    def remove_if_filled(order, order_book)
+      return unless order.filled?
+      order_book.remove_order(order.id)
+    end
+  end
+end
diff --git a/lib/rex/order_book.rb b/lib/rex/order_book.rb
index ed2c124..2b38845 100644
--- a/lib/rex/order_book.rb
+++ b/lib/rex/order_book.rb
@@ -6,6 +6,7 @@ module Rex
       @sell_side = RBTree.new
       @buy_side = RBTree.new
       @order_ids = {} # order_id => order
+      @current_trade_id = 0
     end
 
     def add_order(order)
@@ -49,6 +50,10 @@ module Rex
       sell_side.first&.[](0)
     end
 
+    def next_trade_id
+      @current_trade_id += 1
+    end
+
     private
 
     attr_reader :order_ids, :buy_side, :sell_side
diff --git a/lib/rex/trade.rb b/lib/rex/trade.rb
new file mode 100644
index 0000000..6c9db0d
--- /dev/null
+++ b/lib/rex/trade.rb
@@ -0,0 +1,19 @@
+module Rex
+  class Trade
+    attr_accessor(
+      :id,
+      :buy_order,
+      :sell_order,
+      :amount,
+      :price
+    )
+
+    def initialize(attributes = {})
+      @id = attributes[:id]
+      @buy_order = attributes[:buy_order]
+      @sell_order = attributes[:sell_order]
+      @amount = attributes[:amount]
+      @price = attributes[:price]
+    end
+  end
+end
diff --git a/spec/matcher_spec.rb b/spec/matcher_spec.rb
new file mode 100644
index 0000000..65a2ca5
--- /dev/null
+++ b/spec/matcher_spec.rb
@@ -0,0 +1,53 @@
+# frozen_string_literal: true
+
+RSpec.describe Rex::Matcher do
+  let(:instance) { described_class.new }
+
+  describe "#match" do
+    let(:order_book) { Rex::OrderBook.new }
+    let(:buy_order) { build(:order, price: 100, is_buy: true, amount: 100, remaining_amount: 100) }
+    let(:cheaper_sell_order) { build(:order, price: 99, is_buy: false, amount: 50, remaining_amount: 50) }
+    let(:pricier_sell_order) { build(:order, price: 100, is_buy: false, amount: 70, remaining_amount: 70) }
+
+
+    context "when order book has unmatched orders" do
+      before do
+        order_book.add_order(buy_order)
+        order_book.add_order(cheaper_sell_order)
+        order_book.add_order(pricier_sell_order)
+      end
+
+      it "returns proper trades" do
+        trades = instance.match(order_book)
+
+        expect(trades.length).to eq(2)
+
+        expect(trades[0].id).to eq(1)
+        expect(trades[0].buy_order).to eq(buy_order)
+        expect(trades[0].sell_order).to eq(cheaper_sell_order)
+        expect(trades[0].price).to eq(99)
+        expect(trades[0].amount).to eq(50)
+
+        expect(trades[1].id).to eq(2)
+        expect(trades[1].buy_order).to eq(buy_order)
+        expect(trades[1].sell_order).to eq(pricier_sell_order)
+        expect(trades[1].price).to eq(100)
+        expect(trades[1].amount).to eq(50)
+      end
+
+      it "removes filled orders from the order book" do
+        instance.match(order_book)
+
+        expect(order_book.highest_buy_order).to eq(nil)
+        expect(order_book.lowest_sell_order).to eq(pricier_sell_order)
+        expect(order_book.lowest_sell_order.remaining_amount).to eq(20)
+      end
+    end
+
+    context "when order book is empty" do
+      it "returns an empty list" do
+        expect(instance.match(Rex::OrderBook.new)).to eq([])
+      end
+    end
+  end
+end
diff --git a/spec/order_book_spec.rb b/spec/order_book_spec.rb
index cdafc0f..f7f869e 100644
--- a/spec/order_book_spec.rb
+++ b/spec/order_book_spec.rb
@@ -94,4 +94,12 @@ RSpec.describe Rex::OrderBook do
       end
     end
   end
+
+  describe "#next_trade_id" do
+    it 'returns an increasing trade id' do
+      expect(instance.next_trade_id).to eq(1)
+      expect(instance.next_trade_id).to eq(2)
+      expect(instance.next_trade_id).to eq(3)
+    end
+  end
 end